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From the top of a 100 foot high pole, an observer measures the angle of depression of a car on the road as 28
degrees.

Find, to the nearest hundredth of a foot, the distance from the car to the base of the pole.

Sagot :

Answer:  approximately 188.07 feet

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Explanation:

Refer to the diagram below. Note that the 62 degree angle is from the fact that 90-28 = 62.

With the reference angle 62 degrees in mind, we have an unknown opposite side x feet and a known adjacent side 100 feet.

Use the tangent trig ratio to tie the two sides together, and then solve for x.

tan(angle) = opposite/adjacent

tan(62) = x/100

100*tan(62) = x

x = 100*tan(62)

x = 188.072646534633 approximately

x = 188.07 feet approximately

Your calculator needs to be in degree mode. One way to check is to compute something like tan(45) and the result should be 1.

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