Question

John is standing on top of a cliff 275 feet above the ocean. The measuremment of the angle of depression to a boat in the ocean is 38 degrees. How far is the boat from the base of the cliff?

Answer 1

352m

Explanation:

h = 275m

a = b (alternative angles)

.: b = 38°

Let the base from the boat to the cliff be d

Using Tan

Tan 38° = opposite ÷ adjacent

Tan 38° ° = 275 ÷d

d = 275 ÷ Tan 38 °

d = 352m

.: The boat is 352m away from the foot of the cliff

Answer 2

Answer: The boat is approximately 357.4 feet from the base of the cliff.

Explanation:

Let x be the horizontal distance from the base of the cliff to the boat. Using the tangent function, we can write:

tan(38) = 275 / x

Solving for x, we have:

x = 275 / tan(38)

Using a calculator, we get:

x ≈ 357.4 feet

Therefore, the boat is approximately 357.4 feet from the base of the cliff.