Numeric Response
Numeric Response
1. A rope that anchors a hot air balloon to the ground is $145 \mathrm{~m}$ long. The balloon is $92 \mathrm{~m}$ above the ground. The angle of elevation of the rope, to the nearest degree, is
(Record your answer in the numerical-response section below.)
Your answer:

Step 1 ：This problem involves trigonometry. We can use the tangent function to solve it. The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side. In this case, the opposite side is the height of the balloon above the ground, and the adjacent side is the length of the rope.

Step 2 ：We can use the arctangent function (also known as the inverse tangent function) to find the angle.

Step 3 ：Let's denote the length of the rope as \(rope\_length = 145\) and the height of the balloon as \(height = 92\).

Step 4 ：Calculate the angle in radians using the formula \(angle\_rad = atan(height / rope\_length)\), which gives us \(angle\_rad = 0.565389334448601\).

Step 5 ：Convert the angle from radians to degrees using the formula \(angle\_deg = angle\_rad * (180 / \pi)\), which gives us \(angle\_deg = 32.3944226456154\).

Step 6 ：Round the angle to the nearest degree to get \(angle\_deg\_rounded = 32\).

Step 7 ：Final Answer: The angle of elevation of the rope, to the nearest degree, is \(\boxed{32}\).