Question

23. The pilot of a small private plane can look forward and see the control tower for a small airstrip.

Beyond that is a large factory that is 4.8 miles from the airstrip. The angles of depression are 13.1°

and 4.1°, respectively. Find the airplane's altitude, to the nearest ten feet.


SHOW WORK

WILL MARK BRANLIEST

Answer 1

Answer:

Altitude of the plane is 0.5 miles.

Step-by-step explanation:

From the figure attached,

An airplane A is at height h miles observes a small airstrip at D and a factory at F, 4.8 miles apart from D.

Angle of depressions for the airstrip is 13.1° and the factory is 4.1°.

We have to calculate the airplane's altitude h.

From ΔABF,

tan4.1 = $\frac{AB}{BF}=\frac{h}{(x+4.8)}$

h = 0.07168(x + 4.8) -----(1)

From ΔABD,

tan13.1 = $\frac{h}{x}$

h = 0.2327x -----(2)

From equation (1) and (2),

0.07168(x + 4.8) = 0.2327x

0.2327x - 0.07168x = 4.8×0.07168

0.161x = 0.344

x = $\frac{0.344}{0.161}=2.14$ miles

From equation (2),

h = 0.2327×2.137

h = 0.4972 miles

h ≈ 0.5 miles

Therefore, 0.5 miles is the altitude of the plane.