Question

A helicopter hovers 500 m above a long straight road. There is a truck to the left and right of the helicopter. The angles of depression of the two trucks from the helicopter are 60° and 20°. How far apart are the two trucks?

Answer 1

1045.01 rounded to the nearest hundredth

Explanation:

First, we can draw this out. The angle of depression is the angle formed by the object at the top and the line formed by the object at the top and the object at the bottom.

If the truck on the left is truck A and the truck on the right is truck B, with the helicopter being the circle on top, there is one 60 degree angle of depression and one 20 degree one. If we make a point at the point in the road the helicopter is straight above, and we connect the points, we can form two right triangles, as shown. If we can calculate the lengths of sides x and y, we can add them up to find the length between the two trucks.

Starting with side x, we know one angle and the side length adjacent to that angle. We want to find the length opposite that angle. One formula that encompasses this is tan(θ) = opposite/adjacent. Therefore, tan(60) = x/500

tan(60) = x/500

multiply both sides by 500 to isolate the x

tan(60) * 500 = x

x = 866.0254

Similarly, with side y, we can say that tan(20) = y/500 and

tan(20) * 500 = y

y= 181.9851

The distance between the two trucks can be shown as x+y, so x+y= 1045.01 rounded to the nearest hundredth