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4) A man standing on a cliff looks down with an angle of depression of 40 degrees to a boat in
the water below the cliff. The cliff is 80m high and the man's eye's are 1.5m above the cliff. How
far from the cliff wall is the boat?

Respuesta :

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:

[tex]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[/tex]

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

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