Question

You are standing on a balcony in a building and need to get out quickly. You are going to drop a rope to the ground, so you can climb down but need to calculate how long the rope should be. Your friend is standing on the ground 30m away from your building and measures the angle of elevation to your balcony to be 80°. How long should the rope be you need to get down from your balcony?

A. Calculate the required length of the rope to descend from the balcony.
B. Determine the rope length needed for a safe descent from the balcony.
C. Find the rope length required when descending from an 80° angle balcony.
D. How long should the rope be for a safe escape from the balcony?

Answer 1

To calculate the required length of the rope to descend from the balcony, we can use the tangent function. The tangent of the angle of elevation is equal to the height of the balcony divided by the distance to your friend on the ground.

Step-by-step explanation:

To calculate the required length of the rope to descend from the balcony, we can use the tangent function. The tangent of the angle of elevation is equal to the height of the balcony divided by the distance to your friend on the ground. Rearranging the equation, we have:

Tan(80°) = height / 30m

Therefore, height = Tan(80°) * 30m

By substituting the value of the tangent, we can calculate the height of the balcony. The length of the rope should be equal to the height of the balcony plus any additional length required to reach the ground safely. So, the required length of the rope should be:

Rope Length = height + additional length

where additional length can be determined based on the actual location of the ground beneath the balcony.