drawbridge at the entrance to an ancient castle is raised and lowered by a pair of chains. The figure represents the drawbridge when flat. Find the height of the suspension point of the chain, to the nearest tenth of a meter, and the measures of the acute angles the chain makes with the wall and the drawbridge, to the nearest degree.
Answers
Answer:
4.0 meters, ∠C = 39°, ∠A = 51°
Step-by-step explanation:
Firstly, our diagram shows us that the given triangle is actually a right triangle. So we can use the Pythagorean Theorem to solve for the height of the chain:
[tex]a^{2} +b^{2} =c^{2}[/tex]
[tex](3.3)^{2} +b^{2} =(5.2)^{2}[/tex]
[tex]b^{2} =(5.2)^{2}-(3.3)^{2}[/tex]
[tex]b =\sqrt{(5.2)^{2}-(3.3)^{2}}[/tex]
[tex]b=4.0187...[/tex]
[tex]b=4.0 m[/tex]
Now, we can use the Law of Cosines to figure out one of the acute angles:
[tex]c^{2} =a^{2} +b^{2} -2ab(cos(C))[/tex]
[tex](3.3)^{2} =(4.0)^{2} +(5.2)^{2} -2(4.0)(5.2)(cos(C))[/tex]
[tex]cos(C)=\frac{(3.3)^{2}-(4.0)^{2} -(5.2)^{2}}{-2(4.0)(5.2)}[/tex]
[tex]C=cos^{-1}( \frac{(3.3)^{2}-(4.0)^{2} -(5.2)^{2}}{-2(4.0)(5.2)})[/tex]
[tex]C=39.3915...[/tex]
∠C = 39°
And since we know that all angles in a triangle add up to 180°:
∠A + ∠B + ∠C = 180
∠A + 90 + 39 = 180
∠A = 180 - 90 - 39
∠A = 51°
However, you should always review any answers on the Internet and make sure they are correct! Check my work to see if I made any mistakes!
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(300*1.55)
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Answer:
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Step-by-step explanation:
Tyler tried to solve an equation step by step
3(x +4)=-18
Answers
Answer:
x = -10
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Step-by-step explanation:
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What is the volume of this container?
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2,125 cm3
5 cm
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Answers
Answer:
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Step-by-step explanation:
hope it helps bye!!
I need help with this, it's due in 15 mins-
Mrs. Carver recorded how much time you and your classmates spent working on helping her with the science lab on Friday. The number of hours each student spent is shown below.
1, 1, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 7
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Answers
Answer:
Mean: 3.5263157894737
Median: 3
Mode: 3
Step-by-step explanation: The mode is 3 because the mode is for which number pops up the most, which is 3.
I got the median by crossing out 8 from the left and the right of the number set and got 3 as the last number.
I got the mean by adding up all the numbers and divided it by the amount of numbers in the set.
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Answers
Answer:
28
Step-by-step explanation
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7x7=49
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Find the distance between the points (-3,14) and (4,-10)
Answers
Answer:
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Step-by-step explanation:
The value of x is ?
Answers
Steps:
(3x + 12) + x = 180
3x + 12 + x = 180
4x + 12 = 180
4x = 180 - 12
4x = 168
x = 168/4
x = 42
Check:
(3x + 12) + x = 180
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126 + 12 + 42 = 180
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I would appreciate the brainliest if this was correct and had helpful & clear steps! :)
The waiting time to ride a roller coaster is 1/3 of an hour when 150 people are in line. How
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Answers
Answer:
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If a sales person receives a commission of 12% of sales what is the sales person commission on a $250,000 sale
Answers
Answer:
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Step-by-step explanation:
250000 * 0.12 = 30000
Which of the following are solutions to the inequality below? TELL ME ALL THE ONES THAT ARE RIGHT.
Answers
Answer:
f = 100 and f = 65
Step-by-step explanation:
[tex]\frac{5}{5} \geq 9 = 1 \geq 9[/tex]
[tex]\frac{100}{5} \geq 9 = 20 \geq 9[/tex] ←
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Answers
Answer: answer is 72 you can get it by either multiplying the height and the base by two and following the formula for area of a triangle or you can divide 36 by two and multiply that by 4
Step-by-step explanation:
Answer:
72 meters
Step-by-step explanation:
Working on 1 triangle at a time
How to find the area of a triangle: Base x Height divided by 2
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36 divided by 2 = 18
Each triangle is 18 meters
18 x 4 triangles = 72 meters
Question 5
3 pts
(6.03)
How many variable terms are in the expression 3x3y + 5x2 + y + 9? (Input a
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Question 6
4 nts
Answers
Answer:
2
Step-by-step explanation:
Is 4/5 greater or less than 45/100 how do you know
Answers
Answer:
4/5 is grater than 45/100
Step-by-step explanation:
Why?
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now to make 4/5 a percentage what times 5 = 100?
20 does
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4*20= 80
now your fraction is 80/100 (top # tells you the %)
it's 80%
80% is grater than 45%
Answer:
4/5 is greater than 45/100.
Step-by-step explanation:
In order to figure it out, you need to make both fractions have common denominators. In order to do that, you figure out this:
5 times what equals 100? It's 20.
With fractions in this situation, whatever you do to the top, you have to do to the bottom. So, you multiply 4 times 20, which is 80.
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Please consider giving me brainliest if this helped you! :)
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Answers
Answer:
9.14532 x 10^8
Step-by-step explanation:
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BC
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А
65°
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B
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Answers
Answer:
90
Step-by-step explanation:
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Step-by-step explanation:
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Answers
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Step-by-step explanation:
x² + 2x - 24 = (x + 6)(x - 4) = x² - 4x + 6x - 24 = x² + 2x - 24
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Answers
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
Answer:
Step-by-step explanation:
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Answers
— x. — = —
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Answers
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Step-by-step explanation:
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Answers
Answer:
57 degrees
Step-by-step explanation:
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Answer:
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Step-by-step explanation:
have a nice day !!
if your looking for the answer to x just divide -56 by 24
...........................
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Answer:
............................
Step-by-step explanation:
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Answer:
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2nd triangle: 48
3rd triangle: 48
4th triangle: 48
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