Question

A pilot in an apache rescue helicopter, at an altitude of 1200 feet, spots his two soldiers on the ground. the angles of depression to the soldiers are 53 and 30. How far apart are the two soldiers, to the nearest foot

Answer 1

`x=1174\ feet`

Explanation:

Right Triangle

It's a special type of triangle where one of its internal angles is 90°. The basic trigonometric formulas apply to relate lengths and angles. If h is the opposite side to the angle \theta, and x is the adjacent side of the same angle, then

`\displaystyle tan\theta =(h)/(x)`

Or, equivalently

`\displaystyle x =(h)/(tan\theta)`

The helicopter, ground and the two soldiers form two right triangles, as shown in the image below. Let's call x1 the distance from soldier 1 to the point O, then

`\displaystyle x_1 =(h)/(tan53^o)`

`\displaystyle x_1 =(1200)/(tan53^o)`

`x_1=904 \ feet`

Now for x2, the distance from soldier 2 to the point O

`\displaystyle x_2 =(1200)/(tan30^o)`

`x_2=2078\ feet`

The distance between the soldiers is

`x=2078\ feet-904\ feet`

`\boxed{x=1174\ feet}`