Question

Sparky the Bear is atop a 100 foot tower. He is looking out over a fairly level area for careless people who might start fires. Suddenly, he sees a fire starting. He marks down the direction of the fire, but he also needs to know how far away the tower is from the fire.

Answer 1

The distance of sparky to the fire is 99.445 feet

Application of SOH CAH TOA identity

Given the following parameters

The angle of depression = 6  degrees

If Sparky is looking over the fairly level, hence the hypotenuse is 100 foot

Required

Distance from spark tower to the fire

Using the expression below

Cos 6 = D/100

D = 100cos6

D = 100(0.9945)
D = 99.45foot

Hence the distance of sparky to the fire is 99.445 feet

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