Question

4) A man standing on a cliff looks down with an angle of depression of 40 degrees to a boat in

Answer 1

Answer:

Distance between boat and cliff (Base) = 97 m (Approx)

Step-by-step explanation:

Given:

Angle of depression = 40°

Height of cliff = 80 m

Height of man's eye's from cliff = 1.5 m

Find:

Distance between boat and cliff (Base) :

Computation:

Total height (Height) = 80 m + 1.5 m = 81.5 m

Using trigonometry application:

$Tan\theta = \frac{Height}{Base} \\\\Tan \ 40 = \frac{81.5}{Base} \\\\Using\ calculator\ to\ find\ the\ value\ of\ Tan 40\\\\Tan 40 = 0.839\\\\0.839=\frac{81.5}{Base}\\\\Base = 97.139$

Distance between boat and cliff (Base) = 97 m (Approx)