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ella [17]
3 years ago
12

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 th

e 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?

Mathematics
1 answer:
olga nikolaevna [1]3 years ago
7 0

Answer:

Height of the stone​ face = 66.29 feet

Step-by-step 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=\frac{AC}{AB}\\\\tan31=\frac{AC}{900}\\\\AC=540.77feet

In ΔABD we have

             tan34=\frac{AD}{AB}\\\\tan34=\frac{AD}{900}\\\\AD=607.06feet

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

Height of the stone​ face = CD = 66.29 feet

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