Question

A man is just about to ski down a steep mountain. He estimates the angle of depression from where he is now to the flag at the bottom of the course to be 24°. He knows that he is 800 feet higher than the base of the course. How long is the path that he will ski? (round to the nearest foot)

Answer 1

Given :-

• the angle of depression from where he is now to the flag at the bottom of the course to be 24°.
• He knows that he is 800 feet higher than the base of the course.

To Find :-

• How long is the path that he will ski? (round to the nearest foot) .

Answer :-

we know that,

→ sin θ = P/H

→ sin 24° = height above base / length of path

→ sin 24° = 800 / length of path

→ length of path = 800 / sin 24°

→ length of path = 800 / 0.4

→ length of path ≈ 2000 feet (Ans.)

Answer 2

Answer:

2000 feet

Step-by-step explanation:

1. Draw the figure:

2. What is given:

• The angle of depression = 24°

• Height for starting point to end = 800 feet

3. Compare the given to the side of the triangle with respect to the given angle:

• Angle of depression = 24°

• Shorter side = 800’

4. What is unknown?

• Distance traveled from the starting point to end? (hypotenuse)

5. Formula:

• $sin(24) = \frac{opposite}{hypotenuse}$

6. Solution:

• $sin (24)=\frac{800}{x}$

• $\frac{(x)sin 24}{sin 24}=\frac{800}{0.4}$
• $x=2000$'