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To measure a stone face carved on the side of a​ mountain, two sightings 900 feet from the base of the mountain are taken. If the angle of elevation to the bottom of the face is 31degrees and the angle of elevation to the top is 34degrees​, what is the height of the stone​ face?

1 Answer

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Answer:

Height of the stone​ face = 66.29 feet

Explanation:

Refer the given figure, here we need to find height of the stone​ face,

Height of the stone​ face = CD

CD = AD - AC

In ΔABC we have


tan31=(AC)/(AB)\\\\tan31=(AC)/(900)\\\\AC=540.77feet

In ΔABD we have


tan34=(AD)/(AB)\\\\tan34=(AD)/(900)\\\\AD=607.06feet

CD = AD - AC = 607.06 - 540.77 = 66.29 feet

Height of the stone​ face = CD = 66.29 feet

To measure a stone face carved on the side of a​ mountain, two sightings 900 feet-example-1
User Mark Edgar
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