Question

The angle of depression from D to F measures 40°. If DE = 100 m, find DF. Round your answer to the nearest tenth.

119.2 m
155.6 m
130.5 m
99.4 m

Answer 1

Option (B) is correct.

DF = 155.6m

Explanation:

Consider Right triangle DEF with right angle at E. Given angle of depression from D to F is 40° that is ∠DFE = 40° and DE = 100 m.

We have to find the value DF.

Using trigonometric ratio,

`\sin F=\frac{\text{Perpendicular}}{\text{Hypotenuse}}`

Here, DF = Hypotenuse and DE = 100

Substitute above ,

`\sin F=(DE)/(DF)`

`\sin 40^(\circ)=(100)/(DF)`

`DF=(100)/(\sin 40^(\circ))`

`DF=(100)/(0.642)`

`DF=155.57`(approx)

Thus, rounding off to nearest tenth DF = 155.6m

Thus, Potion (B) is correct , DF = 155.6 m