Question

A helicopter flying 3,590 feet above the ground spots the top of a 150-foot tall tower. The angle of depression from the helicopter to the top of the building is 83 degrees. How far must the helicopter fly to be directly over the tower?

Answer 1

`x\approx 422.4`

Explanation:

Assuming 'x' the distance helicopter needs to fly to be directly over the tower.

It is given that a helicopter flying 3590 feet above ground spots the top of a 150-foot tall cell phone tower at an angle of depression of 83°.

From attachment that helicopter, tower and angle of depression forms a right triangle.

As height of tower is 150 feet, so the vertical distance between helicopter and tower will be: 3590-150=3440 feet.

Also, the side with length 3590-150 feet is opposite and side x is adjacent side to 83° angle.

As the tangent relates the opposite side of a right triangle to its adjacent side, so we will use tangent to find the length of x.

`\text{Tan}=\frac{\text{Opposite}}{\text{Adjacent}}`

`\text{Tan}(83^o)=(3590-150)/(x)\\`

`\text{Tan}(83^o)=(3440)/(x)`

`x=\frac{3440}{\text{Tan}(83^o)}`=>
`x=(3440)/(8.14434)`

`x\approx 422.4`

Thus, the helicopter must fly approximately 422.4 feet to be directly over the tower.