Question

Chief Sohcahtoa is standing 3500 feet away from a cylindrical mountain. He uses his jet pack to fly to the top of the mountain. He flies with an angle of elevation, relative to the ground, of 15 degrees. How tall is the mountain in feet? Round to the nearest tenth.

Answer 1

Step-by-step

To solve this problem, we'll use the trigonometric function tangent.

The tangent of an angle is equal to the ratio of the opposite side to the adjacent side in a right triangle.

In this case, the opposite side is the height of the mountain, and the adjacent side is the distance Chief Sohcahtoa is standing away from the mountain.

Let's call the height of the mountain "h" and the distance Chief Sohcahtoa is standing "d".

We can use the formula for tangent:

tan(angle) = opposite/adjacent

tan(15°) = h/d

Now, we can rearrange the formula to solve for h:

h = d * tan(15°)

Plugging in the given values:

h = 3500 ft * tan(15°)

Using a calculator:

h ≈ 3500 ft * 0.268

h ≈ 938 ft

Therefore, the height of the mountain is approximately 938 feet.