Question

PLEASE HELP ASAP
A helicopter hovers 500 feet
above a small island. The
figure shows that the angle of
depression from the helicopter
to point P is 48º. How far off
the coast, to the nearest foot, is
the island?
d ft
(Round the answer to the nearest whole number.)

Answer 1

Answer:

d = 450 ft

Step-by-step explanation:

Hi there!

First, we can find the angle in the triangle at the point of the helicopter, the angle opposite $d$. Subtract 48° from 90°:

90-48=42

Now, given that this is a right triangle and we have an angle and the side adjacent the angle, we can solve for $d$ by using the tangent ratio:

$tan\theta=\displaystyle \frac{opposite}{adjacent}$

Replace θ with 42°, "opposite" with $d$, and "adjacent" with 500 ft:

$tan(42)=\displaystyle \frac{d}{500}$

Multiply both sides by 500 to isolate $d$:

$500*tan(42)=d\\450=d$

Therefore, d = 450 ft when rounded to the nearest whole number.

I hope this helps!