PLEASE HELP Solve the right triangle.
Round your answers to the nearest tenth.
Answers
Answer:
A = 40°
a = 9.0
b = 10.7
Step-by-step explanation:
The sum of interior angles of a triangle is 180°
⇒ m∠A + 50° + 90° = 180°
⇒ m∠A + 140° = 180°
⇒ m∠A = 180° - 140°
⇒ m∠A = 40°
[tex]\mathsf{\cos(\theta)=\dfrac{adjacent\ side}{hypotenuse}}[/tex]
Given:
[tex]\theta[/tex] = 50°side adjacent to the angle = ahypotenuse = 14[tex]\implies \mathsf{\cos(50)=\dfrac{a}{14}}[/tex]
[tex]\implies \mathsf{a=14\cos(50)}[/tex]
[tex]\implies \mathsf{a=9.0\ (nearest\ tenth)}[/tex]
[tex]\mathsf{\sin(\theta)=\dfrac{opposite\ side}{hypotenuse}}[/tex]
Given:
[tex]\theta[/tex] = 50°side opposite to the angle = bhypotenuse = 14[tex]\implies \mathsf{\sin(50)=\dfrac{b}{14}}[/tex]
[tex]\implies \mathsf{b=14\sin(50)}[/tex]
[tex]\implies \mathsf{b=10.7\ (nearest\ tenth)}[/tex]
[tex]\bold{\huge{\underline{ Solution }}}[/tex]
Let consider the given triangle be ABC
Here, It is given in the question that ,
[tex]\sf{ {\angle} B = 90° }[/tex][tex]\sf{ {\angle} C = 50° }[/tex][tex]\sf{ AC = 14 }[/tex]Therefore,By using Angle sum property
It states that the sum of all angles of triangles are equal to 180°That is,
[tex]\bold{\pink{ {\angle} A + {\angle}B + {\angle}C = 180{\degree}}}[/tex]
Subsitute the required values,
[tex]\sf{ {\angle}A + 90{\degree} + 50{\degree}\: =\: 180{\degree} }[/tex]
[tex]\sf{ {\angle}A + 140{\degree}\: = \:180{\degree} }[/tex]
[tex]\sf{ {\angle}A\: = \: 180{\degree} - 140{\degree} }[/tex]
[tex]\sf{ {\angle}A \: =\: 40{\degree} }[/tex]
Thus, The angle A is 40°
Now,We have to find the side a and b
We know that,
[tex]\bold{\red{ Sin{\theta} \:=\: }}{\bold{\red{\dfrac{Perpendicular }{Hypotenuse }}}}[/tex]
[tex]\bold{\red{ Cos{\theta} \:=\: }}{\bold{\red{\dfrac{ Base }{Hypotenuse }}}}[/tex]
For side A[tex]\sf{ Sin\: 40 {\degree} \:= \:}{\sf{\dfrac{ a}{ 14 }}}[/tex]
[tex]\sf{ Sin(}{\sf{\dfrac{2{\pi}}{9}}}{\sf{) \:= \:}}{\sf{\dfrac{ a}{14 }}}[/tex]
[tex]\sf{Sin(}{\sf{\dfrac{2{\times} 3.14 }{9}}}{\sf{) \:= \:}}{\sf{\dfrac{ a}{14 }}}[/tex]
[tex]\sf{sin(}{\sf{\dfrac{6.28}{9}}}{\sf{) \:=\: }}{\sf{\dfrac{ a}{14 }}}[/tex]
[tex]\sf{ a \:= \:14 {\times} 0.64}[/tex]
[tex]\sf{ a \: = \:14 {\times} 0.64}[/tex]
[tex]\bold{ a\: =\: 8.96\: \: or \:\:9\:\: (approx) }[/tex]
For Side B[tex]\sf{ Sin\: 50 {\degree} = }{\sf{\dfrac{ b }{ 14 }}}[/tex]
[tex]\sf{Sin(}{\sf{\dfrac{5{\pi}}{18}}}{\sf{)\: =\: }}{\sf{\dfrac{ b}{14 }}}[/tex]
[tex]\sf{Sin(}{\sf{\dfrac{5{\times} 3.14 }{18}}}{\sf{ ) \: = \:}}{\sf{\dfrac{ b}{14 }}}[/tex]
[tex]\sf{Sin(}{\sf{\dfrac{15.7}{18}}}{\sf{ )\: = \:}}{\sf{\dfrac{ b}{14 }}}[/tex]
[tex]\sf{ b\: = \:14 {\times} 0.76}[/tex]
[tex]\bold{ b\: = \: 10.64\:\: or \:\:10.7\:\: (approx) }[/tex]
Hence, The value of angle A , side a and b is 40° , 9 and 10.7 .
Related Questions
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Rita buys a box of chocolates.
(Extra)
For every 2 plain chocolates there are 3 milk chocolates.
There are 30 chocolates in the box.
How many milk chocolates are there?
Show your method
Answers
Answer:
12 plain and 18 milk
Step-by-step explanation:
convert it to fraction first: 2/5 are plain and 3/5 is milk
30÷5= 6
2x6=12
3x6=18
to check wheter or not it is correct add the amount. if it gets the total, it is correct.
Max loves fishing. He and his family chartered a fishing boat that left Florida and traveled towards the Bahama Islands at an
average speed of 10 km/hour. Some time later a cruise ship left traveling in the same direction but at an average speed of 14
km/hour. After traveling for ten hours the cruise ship caught up with the fishing boat. How long did the fishing boat travel before
the cruise ship caught up?
Note: Remember to find the time the fishing boat was traveling not just what x is.
Select the correct response:
28 hours
24 hours
14 hours
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Answers
The fishing boat traveled for 14 hours before the cruise ship caught up.
We have,
Let's assume that the fishing boat traveled for x hours before the cruise ship caught up.
In that time, the fishing boat covered a distance of 10x km.
During the same 10 hours, the cruise ship traveled 14 x 10 = 140 km.
Since both the fishing boat and the cruise ship covered the same distance, we can write:
10x = 140
Solving for x, we get:
x = 14
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If PQ= 18 units, where should the midpoint lie to divide the line segment into two congruent segments?
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Answers
Answer:
They are all 100
Step-by-step explanation:
Each side has a meaning it is the same and all but one have an a. The one that doesnt has 100.
The answer is 100
Have an amazing day!
PLEASE RATE!!
Step-by-step explanation:
Total angle of regular pentagon = 540
4a + 100 = 540
4a = 440
a = 110°
Can anyone tell me what median,mode, and mean is? thanks :)
Answers
Answer:
The mean (average) of a data set is found by adding all numbers in the data set and then dividing by the number of values in the set.
The median is the middle value when a data set is ordered from least to greatest.
The mode is the number that occurs most often in a data set.
Step-by-step explanation:
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Which inequality is represented on the line?
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Answers
Answer:
Ello Haikyuu here!
Step-by-step explanation:
Inequalities on a number line. Inequalities can be represented on a number line as shown in the inequalities below: Note: the open circle above a number means it is not included as part of the solution to the inequality while the solid circle means that it is.
uh I hope this is right, i'm not sure
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The box plots show the number of hours of television a group of middle school students and a group of elementary school students watch each week.
Middle School Students
2 box plots. The number line goes from 0 to 10. For middle school students, the whiskers range from 1 to 9, and the box ranges from 2 to 7. A line divides the box at 4. For elementary school students, the whiskers range from 1 to 9, and the box ranges from 4 to 7. A line divides the box at 5.5.
Elementary School Students
Which are true statements when comparing the data in the box plots? Select three choices.
The data for elementary school are more consistent than those for middle school.
More of the data for middle school lie closer to the median than the data for elementary school.
About 50% of elementary school students watch between 4 and 7 hours of television each week.
About one-half of middle school students watch less than 2 hours of television each week.
On average, middle school students watch less television than elementary school students each week.
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The correct answer is A,C and D
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Answer:
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Step-by-step explanation:
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Answer:
x = -2
Step-by-step explanation:
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[tex]\mathrm{Subtract\:}4\mathrm{\:from\:both\:sides}[/tex]
[tex]\frac{1}{2}x+4-4=3-4[/tex]
[tex]\mathrm{Simplify}[/tex]
[tex]\frac{1}{2}x=-1[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:}2[/tex]
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[tex]\mathrm{Simplify}[/tex]
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[RevyBreeze]
Find the sum of 2+37/8+20/9
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Step-by-step explanation:
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Please help :( On the coordinate grid shown below, pentagon J is similar to pentagon K.
Which sequence of transformations could be applied to pentagon J to create pentagon K?
A. a rotation 90° counterclockwise about the origin, then a translation 3 units up and 7 units right
B. a reflection across the x-axis, then a translation 2 units up and 8 units right
C. a rotation 90° clockwise about the origin, then a translation 1 unit down and 5 units right
D. a reflection across the y-axis, then a translation 4 units right
Answers
Answer:
A
Step-by-step explanation:
i think it's A, i am not 100% sure and i cannot give you a full explanation why because i am doing it in my head, but i mentally did all the other ones and A is the only one that would work
Write an equation in slope intercept form of the line that has a slope of 6 and goes through the point (3,-2)
Answers
Answer: y=6x-20
Step-by-step explanation:
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Which expression is equivalent to 7 2/3 ⋅ 71/4?
A. 7 3/7
B. 7^-1
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Answers
Step-by-step explanation:
D. 7 11/12
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Put the following equation of a line into slope-intercept form, simplifying all fractions. 4x+4y=4
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Step-by-step explanation:
1. Martha can complete 15 activities a day at summer camp. She can choose between crafts or sports.
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art
Step-by-step explanation:
What is the following quotient? StartFraction 2 Over StartRoot 13 EndRoot StartRoot 11 EndRoot EndFraction.
Answers
Function assigns one element of one set to the other specific element of another set. The quotient of the fraction [tex]\dfrac{2}{\sqrt{13}+\sqrt{11}}[/tex] is [tex]{\sqrt{13}-\sqrt{11}}[/tex].
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
As the fraction is given to us,
[tex]\dfrac{2}{\sqrt{13}+\sqrt{11}}[/tex]
Rationalizing the fraction we will get,
[tex]=\dfrac{2}{\sqrt{13}+\sqrt{11}} \times \dfrac{{\sqrt{13}-\sqrt{11}}}{{\sqrt{13}-\sqrt{11}}}\\\\= \dfrac{2({\sqrt{13}-\sqrt{11}})}{(\sqrt{13})^2-(\sqrt{11})^2}\\\\= \dfrac{2({\sqrt{13}-\sqrt{11}})}{13-11}\\\\=\dfrac{2({\sqrt{13}-\sqrt{11}})}{2}[/tex]
Now, if we divide the numerator by the denominator to get the quotient we will get,
[tex]= \dfrac{2({\sqrt{13}-\sqrt{11}})}{2}\\\\={2({\sqrt{13}-\sqrt{11}})}\div 2\\\\={\sqrt{13}-\sqrt{11}}[/tex]
Hence, the quotient of the fraction [tex]\dfrac{2}{\sqrt{13}+\sqrt{11}}[/tex] is [tex]{\sqrt{13}-\sqrt{11}}[/tex].
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The quotient of the given number start Fraction 2 over start root 13 end root start root 11 end root end Fraction.
[tex]\sqrt{13}-\sqrt{11}[/tex]
What is the quotient?Quotient is the resultant number which is obtained by dividing a number with another. Let a number a is divided by number b. Then the quotient of these two number will be,
[tex]q=\dfrac{a}{b}[/tex]
Here, (a, b) are the real numbers.
The number Start Fraction 2 Over Start Root 13 End Root Start Root 11 End Root End Fraction given can be written as,
[tex]\dfrac{2}{\sqrt{13}+\sqrt{11}}[/tex]
Let the quotient of this division is n. Therefore,
[tex]n=\dfrac{2}{\sqrt{13}+\sqrt{11}}[/tex]
By rationalizing the denominator, we get,
[tex]n=\dfrac{2}{\sqrt{13}+\sqrt{11}}\times\dfrac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}\\n=\dfrac{2(\sqrt{13}-\sqrt{11})}{(\sqrt{13})^2-(\sqrt{11})^2}\\n=\dfrac{2(\sqrt{13}-\sqrt{11})}{13-11}\\\\n=\dfrac{2(\sqrt{13}-\sqrt{11})}{2}\\n=\sqrt{13}-\sqrt{11}[/tex]
Hence, the quotient of the given number start Fraction 2 Over Start Root 13 End Root Start Root 11 End Root End Fraction.
[tex]\sqrt{13}-\sqrt{11}[/tex]
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Answers
Answer:
[tex]x(x {}^{2} - 8x - 20) = 0[/tex]
Use the quadratic formula to simply the second degree equation;
[tex]x(x + 2)(x - 10)[/tex]
[tex]x1 = 0[/tex]
[tex]x2 = - 2[/tex]
[tex]x3 = 10[/tex]
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Use the formula y=mx+b to help you convert problems like this into slope - intercept form.
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11,928/1,988 = x/1
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Answer:
6/1 GO GO GO
Step-by-step explanation:
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Give an example of an x-intercept from a vertex form equation.
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Question Below However i have to fill in the 20 characters so yeah comment the answer
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Using proportions, it is found that the change in 2007 was about 5.07 times greater than the change is 2000.
What is a proportion?A proportion is a fraction of a total amount. Using it, to find how many times a measure a is greater than a measure b, we divide a by b.
In this problem:
In 2007, the change was of $0.71.In 2000, the change was of $0.14.Hence:
$0.71/$0.14 = 5.07.
The change in 2007 was about 5.07 times greater than the change is 2000.
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Hich of the following is equivalent to 5 square root 13^3?
Answers
Answer:
I believe the answer is 65 square root 13, if im wrong pls give me the options to choose from
n - 5 = 3n + 1
solve for n.
Answers
Answer:
-3
Step-by-step explanation:
n-5=3n+1
3n-n= -5-1
2n= - 6
n=-3
Someone please help im on timed test
What is the quotient of 7.92 times 10^7 and 7.2 times 10^3 expressed in scientific notation?
Answers
Given parameters:
First number = 7.92 x 10⁷
Second number = 7.2 x 10³
Quotient is the number obtained division;
Now;
[tex]\frac{7.92 x 10^{7} }{7.2 x 10^{3} }[/tex]
= [tex]\frac{7.92}{7.2}[/tex] x 10⁷⁻³
= 1.1 x 10⁴
The quotient of the two numbers expressed in scientific notation is 1.1 x 10⁴
jessica's fish tank has 19 liters of water in it. she plans to add 5 liters per minute until the tank has more than 59 liters. what are the possible numbers of
minutes jessica could add water?
use t for the number of minutes.
write your answer as an inequality solved for t.
Answers
Answer:
8 minutes.
Step-by-step explanation:
Using ' t ' for the number of minutes.
" 59 > 19 + 5t "
→ Solve for t...
= 59 > 19 + 5t
= 59 - 19 > 5x
= 40 > 5t
= 40/5 > t
= 8 > t
Thus, It will take 8 minutes to add 59 litres of water.
19+5t>59
5t>59-19
5t>40
t>8
PLS HELP ASAP THANKS ILL GIVE BRAINLKEST PLS THANKS PLS ASAP PLS
Answers
Answer:
i think its the first one
Answer:
-1 vertical, 5 horizontal
Step-by-step explanation:
On the y-axis, the shape has moved down 1, which is –1 vertical.
On the x-axis, the shape has moved right 5, which is 5 horizontal.
how to solve matrix addition and subtraction
Answers
Answer:
Step-by-step explanation:
[tex]\left[\begin{array}{ccc}1&3&3\\-4&3&3\end{array}\right] -\left[\begin{array}{ccc}4&-3&4\\-1&5&0\end{array}\right] =\left[\begin{array}{ccc}1-4&3+3&3-4\\-4+1&3-5&3-0\end{array}\right] =\left[\begin{array}{ccc}-3&6&-1\\-3&-2&3\end{array}\right][/tex]
Which of the following statements is NOT true?
The rate of change and the constant of proportionality are the same value in a proportional relationship.
The value of and the value of Ay are different in a proportional relationship.
A proportional relationship is a linear relationship.
The unit rate and the k-value are the same value in a proportional relationship.
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Answers
According to an article, 75% of high school seniors have a driver's license. Suppose we take a random sample of 300 high school seniors and find the proportion who have a driver's license. Find the probability that more than 77% of the sample have a driver's license. Begin by verifying that the conditions for the Central Limit Theorem for Sample Proportions have been met
Answers
Using the normal distribution and the central limit theorem, it is found that there is a 0.2119 = 21.19% probability that more than 77% of the sample have a driver's license.
Normal Probability DistributionIn a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
It measures how many standard deviations the measure is from the mean. After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.By the Central Limit Theorem, for a proportion p in a sample of size n, the sampling distribution of sample proportion is approximately normal with mean [tex]\mu = p[/tex] and standard deviation [tex]s = \sqrt{\frac{p(1 - p)}{n}}[/tex], as long as [tex]np \geq 10[/tex] and [tex]n(1 - p) \geq 10[/tex].In this problem, we have that:
75% of high school seniors have a driver's license, hence p = 0.75.A sample of 300 is taken, hence n = 300.The conditions are verified because:
np = 300 x 0.75 = 225 > 10.
n(1-p) = 300 x 0.25 = 75 > 10.
The mean and the standard error are given by:
[tex]\mu = p = 0.75[/tex]
[tex]s = \sqrt{\frac{p(1 - p)}{n}} = \sqrt{\frac{0.75(0.25)}{300}} = 0.025[/tex]
The probability that more than 77% of the sample have a driver's license is one subtracted by the p-value of Z when X = 0.77, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{0.77 - 0.75}{0.025}[/tex]
Z = 0.8
Z = 0.8 has a p-value of 0.7881.
1 - 0.7881 = 0.2119.
0.2119 = 21.19% probability that more than 77% of the sample have a driver's license.
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