Question

Suppose you are standing 19 feet from the base of a flagpole. You are able to determine that the angle of elevation to the top of the pole is 64.60 . Determine the height of the flagpole.

Answer 1

40 ft

Explanation:

Given that the angle of elevation is 64.6°, this means that the angle of depression from the top of the flagpole is 180 - 90 - 64.6, which is 25.4°

We can solve by using the sine rule, or the cosine rule.

Using the sine, we have

Sinθ = OPP/HYP, we're going to use the angle of depression, and thus

Sin 25.4° = 19/x, on rearranging, we have

x = 19/ sin 25.4°

x = 19/0.4289

x = 44.30 ft.

Now, we use Pythagoras theorem to get the height of the flagpole.

44.3² = 19² + y²

y² = 44.3² - 19²

y² = 1962.49 - 361

y² = 1601.49

y = √1601.49

y = 40 ft