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

Answer:

Option (B) is correct.

DF = 155.6m

Step-by-step 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 ,

$\sin F=\frac{DE}{DF}$

$\sin 40^{\circ}=\frac{100}{DF}$

$DF=\frac{100}{\sin 40^{\circ}}$

$DF=\frac{100}{0.642}$

$DF=155.57$(approx)

Thus, rounding off to nearest tenth DF = 155.6m

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