Question

The pilot of a helicopter hovers at an altitude of 1200 feet over a park. the angle of depression to the base of a statue is 17 degrees. the angle of depression to the nearest park exit, in line with the statue, is 14 degrees. to the nearest foot, what is the distance from the statue to the exit?

Answer 1

Here we can use the concept of Height and distance

so here we know that

$Height = 1200 ft$

angle of depression at the foot of the statue is 17 degree

angle of depression at the exit gate is 14 degree

So here the distance of foot of the statue is related as

$\frac{h}{d_1} = tan17$

so here we will have

$d_1 = \frac{h}{tan17}$

$d_1 = \frac{1200}{tan17}$

$d_1 = 3925 ft$

similarly for exit gate the distance is given as

$d_2 = \frac{h}{tan14}$

$d_2 = \frac{1200}{tan14}$

$d_2 = 4813 ft$

now the distance between gate and foot of statue is given as

$d_2 - d_1 = 4813 - 3925$

$d = 888 ft$