Answer:
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