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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?

Respuesta :

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

             [tex]tan31=\frac{AC}{AB}\\\\tan31=\frac{AC}{900}\\\\AC=540.77feet[/tex]

In ΔABD we have

             [tex]tan34=\frac{AD}{AB}\\\\tan34=\frac{AD}{900}\\\\AD=607.06feet[/tex]

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

Height of the stone​ face = CD = 66.29 feet

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