An evergreen tree is supported by a wire extending from 1.5 feet below the top of the tree to a stake in the ground. The wire is 24 feet long and forms a 58° angle with the ground. how tall is the tree?
Answers
Answer:
Approximately [tex]21.9\; \rm ft[/tex] (assumption: this tree is perpendicular to the ground.)
Step-by-step explanation:
Refer to the diagram attached (not drawn to scale.)
Label the following points:
[tex]\rm S[/tex]: stake in the ground.[tex]\rm A[/tex]: top of the tree.[tex]\rm B[/tex]: point where the wire is connected to the tree. [tex]\rm C[/tex]: point where the tree meets the ground.Segment [tex]\rm SB[/tex] would then denote the wire between the tree and the stake. The question states that the length of this segment would be [tex]24\; \rm ft[/tex]. Segment [tex]\rm AB[/tex] would represent the [tex]1.5\; \rm ft[/tex] between the top of this tree and the point where the wire was connected to the tree.
The question is asking for the height of this tree. That would correspond to the length of segment [tex]\rm AC[/tex].
If this tree is perpendicular to the ground, then [tex]\rm \angle A\hat{C}S =90^\circ[/tex]. Triangle [tex]\rm \triangle BCS[/tex] would be a right triangle with segment [tex]\rm SB[/tex] as the hypotenuse.
The question states that the angle between the wire (segment [tex]\rm SB[/tex]) and the ground (line [tex]\rm SC[/tex]) is [tex]58^\circ[/tex]. Therefore, [tex]\rm \angle A\hat{S}C = 58^\circ[/tex].
Notice, that in right triangle [tex]\rm \triangle BCS[/tex], segment [tex]\rm BC[/tex] is the side opposite to the angle [tex]\rm \angle B\hat{S}C = 58^\circ[/tex]. Therefore, the length of segment [tex]\rm BC\![/tex] could be found from the length of the hypotenuse (segment [tex]\rm SB[/tex]) and the cosine of angle [tex]\rm \angle B\hat{S}C = 58^\circ\![/tex].
[tex]\displaystyle \cos\left(\rm \angle B\hat{S}C\right) = \frac{\text{length of $\mathrm{BC}$}}{\text{length of $\mathrm{SB}$}} \quad \genfrac{}{}{0em}{}{\leftarrow\text{opposite}}{\leftarrow \text{hypotenuse}}[/tex].
Rearrange to obtain:
[tex]\begin{aligned}& \text{length of $\mathrm{BC}$} \\ &= (\text{length of $\mathrm{SB}$}) \cdot \cos\left(\angle \mathrm{B\hat{S}C}\right)\\ &= \left(24\; \rm ft\right) \cdot \cos\left(58^\circ\right) \approx 20.35\; \rm ft\end{aligned}[/tex].
In other words, the wire is connected to the tree at approximately [tex]20.3\; \rm ft[/tex] above the ground.
Combine that with the length of segment [tex]\rm AB[/tex] to find the height of the entire tree:
[tex]\begin{aligned}&\text{height of the tree} \\ &= \text{length of $\mathrm{AC}$} \\ &= \text{length of $\mathrm{AB}$} + \text{length of $\mathrm{BC}$}\\ &\approx 20.35\; \rm ft + 1.5\; \rm ft \\ &\approx 21.9\; \rm ft\end{aligned}[/tex].
Related Questions
Please answer this correctly without making mistakes
Answers
Answer:
$25-$9.9
Step-by-step explanation:
45/100
0.45*$25
$9.9
$25-$9.9
it cost 14.1
A function, f left parenthesis x right parenthesis comma models the depth of water in a wading pool that is filling at a rate of 11 gallons per minute. Which of these describes why f left parenthesis x right parenthesis can be considered a linear function? I. For every 1 minute interval, the depth of water in the wading pool increases by the same amount. II. The function grows by equal factors every minute. III. The slope of the function is constant.
Answers
Answer:
quiz let or brainy helps me just look up the chapter question and you will get the answer
Step-by-step explanation:
hope this helps
f(x) can be considered as a linear function because of the following conclusions -
1 → For every 1 minute interval, the depth of water in the wading pool increases by the same amount of 11 gallons/minute.
2 → The slope of the function is constant.
What is the general equation of a straight line?
The general equation of a straight line is -
y = mx + c
Where -
[m] is the slope of the line.
[c] is the y - intercept.
Given is the following statement representing a function - f(x), that models the depth of water in a wading pool that is filling at a rate of 11 gallons per minute.
Assume that we represent the depth of the water rate by [y] and the time in minutes by [m]. We can write the function f(x) as -
y = f(x) = 11m
This is a linear relation and its graph will be a straight line passing through origin.
From this equation, we can make the following conclusions -
1 → For every 1 minute interval, the depth of water in the wading pool increases by the same amount of 11 gallons/minute.
2 → The slope of the function is constant.
Therefore, f(x) can be considered as a linear function because of the following conclusions -
1 → For every 1 minute interval, the depth of water in the wading pool increases by the same amount of 11 gallons/minute.
2 → The slope of the function is constant.
To solve more questions on straight line graphs, visit the link below-
brainly.com/question/2954112
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plz help! will give brainliest!!
Answers
Answer:
D) 18 units
Step-by-step explanation:
The ratio is
2 : 3
The actual number values are
12 : ?
Divide 12 by 2 (square A's side) = 6
Multiply 6 by 3 (square B's side) = 18
The right hexagonal pyramid has a hexagon base with equal-length sides. The lateral faces of the pyramid are all triangles (that are exact copies of one another) with heights of 18 ft. Find the surface area of the pyramid.
Answers
Answer:
208
Step-by-step explanation:
The answer is 208 first I multiplied 18x8=144 than 8ft*5=40
40+8=48 than I did 40 +24=64 after that I added 144+64=208 so surface area of the pyramid will be 208ft2
Answer:
352
Step-by-step explanation:
I NEED HELP WHAT IS THE ANSWER FOR PART (A) AND PART (B) I’ll cash app or Venmo if I give me answers by today please help.
Answers
Answer:
9/2 is the slope of the graphed line.
The second statement is true.
Step-by-step explanation:
Factor x3 + 2x2 + x completely.
Answers
Answer:
[tex] {x}^{3} + 2 {x}^{2} + x[/tex]
[tex]x(x {}^{2} + 2x + 1)[/tex]
[tex]x(x + 1) {}(x + 1)[/tex]
[tex]x(x + 1) {}^{2} [/tex]
Answer:
C. x(x+1)2 on edu 2021
Step-by-step explanation:
will give brainliest!
Answers
Answer:
2/1=2
Step-by-step explanation:
please fast tell me
Answers
Answer:
1). Option (b)
2). Option (d)
3). Option (d)
Step-by-step explanation:
Question (1)
For Pythagoras triplet,
(Largest number)² = (Number 1)² + (Number 2)²
a). 5² = 5² + 2²
25 = 25 + 4
25 = 29
Not True.
b). 5² = 3² + 4²
25 = 9 + 16
25 = 25
True.
c). 10² = 1² + 5²
100 = 1 + 25
100 = 26
Not true.
d). 2² = 2²+ 2²
4 = 4 + 4
4 = 8
Not true.
Therefore, Option (b) is correct.
Question (2)
1 - [tex]\frac{1}{5}[/tex] = [tex]\frac{5}{5}-\frac{1}{5}[/tex]
= [tex]\frac{5-1}{5}[/tex]
= [tex]\frac{4}{5}[/tex]
Therefore, Option (d) is the answer.
Question (3)
Property of triangle → Sum of lengths of two sides of a triangle should be greater than the measure of third side.
a). 6 + 3 > 2 ⇒ 9 > 2 [True]
6 + 2 > 3 ⇒ 8 > 3 [True]
2 + 3 > 6 ⇒ 5 > 6 [False]
Triangle is not possible.
b). 2 + 8 > 3 → 10 > 3 [True]
8 + 3 > 2 → 11 > 2 [True]
2 + 3 > 8 → 5 > 8 [False]
Triangle is not possible.
c). 5.5 + 2.5 > 2.5 → 8 > 2.5 [True]
5.5 + 2.5 > 2.5 → 8 > 2.5 [True]
2.5 + 2.5 > 5.5 → 5 > 5.5 [False]
Triangle is not possible.
d). 3 + 6 > 7 → 9 > 7 [True]
3 + 7 > 6 → 10 > 6 [True]
7 + 6 > 3 → 13 > 3 [True]
These are the sides of a triangle.
Therefore, Option D is the answer.
Please help pleaseeeeeeeeeeeeeeee
Answers
Answer:
y=2x+5
Step-by-step explanation:
This is a proportional relationship.The other one's are not true.
PLS Mark brainlist
Hope this helps:)
What is the answer to this radical functions equation ASAP
Answers
Hope it help
Mark Brainly
given that a||b and m<6 is 1/8 of m<4, find m<4 and m<6
Answers
Answer:
Supplementary Angles: if both angles are added = 180 °
Complementary Angles: if both angles are added = 90°
Step-by-step explanation:
Answer:
m<6 = 20*, m<4 = 160*
Step-by-step explanation:
2.m<6+m<4=180*
3. m<6+m<4=180*
4. m<6+8 x m<20
5.m<6 = 20*, m<4 = 160*
Given the quadratic equation: 1/2x^2+3x−10=0
Answers
Answer:
x=2.3851648071345037,−8.385164807134505
Step-by-step explanation:
-3/5a=2
a= ___ please help
Answers
Answer:
a=-3 1/3
Step-by-step explanation:
A store has two different brands of laundry
Answers
Answer:
Step-by-step explanation:
I am sorry but please give detailed question
Answer:
Is there supposed to be a pic?
Step-by-step explanation:
solve y (1/2)y+6=(3/4)y–4
Answers
Answer:
Y = 40
Step-by-step explanation:
Change 1/2 to 2/4
2/4 y + 6 = 3/4y - 4
subtract 2/4y
6 = 1/4y -4
add 4
10 = 1/4y
multiply by 4 to get fraction to 1y or y
y = 40
I GOT IT RIGHT ON MY QUIZ
Draw a line representing the “rise” and a line representing the “run” of the line. State the slope of the line in the simplest form. PLZZ HELPP
Answers
A quantity of food would last a family of 5 for 21days. How long would the same quantity last a family of 7 if they all eat at the same rate?
Answers
5x21=105 the amount of food they have
105/7=15 days of food for a family of 7
How to multiply Decimals by power of 10?
Answers
Answer:
maybe this well help
Step-by-step explanation:
When you multiply a decimal by a power of 10, simply move the decimal place to the right as many places as there are 0s in the power of 10. When you divide a decimal by a power of 10, simply move the decimal place to the left as many places as there are 0s in the power of 10.
Answer:
You can convert the power of 10 to a decimal and multiply it by 0.502, or you can move the decimal place of 0.502 to the left depending on the value of the exponent:
0.502 x 10^2=0.00502 → 10^2 is equal to 100. So, 0.502 x 100=0.00502 OR 10 is raised to a power of 2, so move the decimal place 2 times to get 0.00502.
0.502 x 10^3=0.000502 → 10^3 is equal to 1000. So, 0.502 x 1000=0.000502 OR 10 is raised to a power of 3, so move the decimal place 3 times to get 0.000502.
Hope you understand and that this helps with your question! :)
What is the measure ofEGE?
What is the measure ofCGF?
E
50
F
options for EGF are 40, 55, 65, 80
options for CGF are 50, 90, 95, 115
Answers
Step-by-step explanation:
Angle EGF = 0.5(180° - 50°) = 65°.
Angle CGF = 180° - Angle EGF = 115°.
1) 16% of what number is 14?
2) 52 is what percent of 156
Answers
Answer: first one answer is 2.24
second one answer is 81.12
h(n)=3n-4 find h(-6)
Answers
Answer:
h(-6) = -22
Step-by-step explanation:
h(n) = 3n - 4
h(-6)= 3(-6) - 4
= -18 - 4
= -22
Three vehicles recorded the following information about their trips.
Van: 500 miles in 7.5 hours
Truck: 300 miles in 5 hours
Car: 400 miles in 5.5 hours
Find the unit rate of miles/hour for the Van.
Answers
Answer:96km in 1 hour requires a speed of 96km/h; 96km in 2 hours requires a speed of 96/2=48km/h.
You can travel at any speed between 48km/h and 96km/h to arrive in between 1 and 2 hours.
There is no sufficient info to solve the problem and answer the question.
Also, this fragment "Two bikers started at the same," is a nonsense, not allowable in Math.
Find the antiderivative of the velocity function.
1 rotation = 2pi radians = 2*3.14 radians = 6.28 radians
1 rotation per 8 seconds is the angular velocity 2pi%2F8 radians per second = 6.28%2F8 = 0.785 radians per second
hope this is helpful
By what percent is 16 greater than 12.
Answers
Answer:
28 i assume.
Answer:
The answer is 28% :))
What are the coordinates of the image after point (4,-5) is reflected across the x-axis
Answers
Answer and Step-by-step explanation:
The x-axis is a horizontal line
^
|
|
(<-------------------------|-----------------------------> x
| ^ This line is the x-axis
|
V
^
|
|
(<---------------|--|--|--|--|--|--|--|--|--|--|---------> x
|
|
|
|
| A ● (4, -5)
V
The point is listed, labeled as A. To reflect, all we have to do is go up twice the absolute amount of the y value, so the absolute value of 5 times 2.
^
| A' ● (4, 5)
|
|
|
|
(<---------------|--|--|--|--|--|--|--|--|--|--|---------> x
|
|
|
|
| A ● (4, -5)
V
This new point is labelled as A'.
(4, 5) is the new coordinate.
#teamtrees #WAP (Water And Plant)
Which gives the correct values for points A, B, C, and D? A number line going from negative 2 to negative 1. There are 5 equal spaces between the numbers. A = negative 1 and one-fifths, B = negative 1 and two-fifths, C = negative 1 and three-fifths, D = negative 1 and four-fifths A = negative 1 and one-fifths, B = negative 1 and four-fifths, C = negative 1 and three-fifths, D = negative 1 and two-fifths A = negative 1 and four-fifths, B = negative 1 and three-fifths, C = negative 1 and two-fifths, D = negative 1 and one-fifth A = negative 1 and four-fifths, B = negative 1 and one-fifth, C = negative 1 and three-fifths, D = negative 1 and two-fifths
or if you dont feel like reading all thaaaat-
Answers
Answer:
Step-by-step explanation:
(D).
A mercury thermometer records a temperature of 10°F at 9 a.m. If the temperature drops by 3°F every hour, what will be the temperature by 2 p.m.?
Answers
Answer:
No
Step-by-step explanation:
Help me graph this inequality
Answers
Answer:
Step-by-step explanation:
is 1/3, 7/21 proportion
Answers
Answer:
1/3
Step-by-step explanation:
A rotating wind turbine has a diameter of about 145 feet and its circumference is about 456 feet. A smaller model of the turbine has a circumference of about 16 feet. What will the diameter of the model be? If necessary, round to the nearest whole number.
The diameter of the model will be about ___ feet
Answers
Answer:
ross-multiplication.
circumference divided by the diameter
10/x = 580/185
10x185=1850
1850/580=3.189
Step-by-step explanation:
give me brainliest
Answer:
7 feet.
Step-by-step explanation:
Solve
Set up a proportion using the given information for the turbine and its model.C /d =
C /d
Set up a proportion.660 /210 =
22/ d
Substitute the given values.660 ÷ 30
210 ÷ 30 ≈
22/ d
Since 660 divided by 30 is approximately 22, divide 210 by 30 to find the value of d.
660 /210 ≈
22/ 7
d ≈ 7
The diameter of the model is approximately 7 feet.
A Polynomial, p(x), has zeros when x = -2, x = 1/3, X = 3. What could be the equation of p(x)?
Answers
Answer:
(x+2)(x-1/3)(x-3)
Step-by-step explanation:
This could be a possible equation, the signs of the of the roots are always the opposite in the equation form.