Question

A flagpole is 50 feet from a point on the ground. The angle of depression from the top of the flagpole to the same point on the ground is 40°. Calculate the height of the flagpole to the nearest foot

Answer 1

check the picture below.

make sure your calculator is in Degree mode.

Answer 2

42 feet.

Explanation:

We have been given that a flagpole is 50 feet from a point on the ground. The angle of depression from the top of the flagpole to the same point on the ground is 40°.

We can see from the attachment that side 50 is adjacent and side h is opposite side to angle 40 degrees.

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

`\text{tan}(40^(\circ))=(h)/(50)`

`\text{tan}(40^(\circ))*50=(h)/(50)*50`

`0.839099631177*50=h`

`41.95498155=h`

`h=41.95498155`

`h\approx 42`

Therefore, the height of the flagpole is 42 feet.