Acertain rock rises almost straight upward from the valley floor. from one point, the angle of elevation of the top of the rock is 19.4degrees. from a point 117 m closer to the rock, the angle of elevation of the top of the rock is 37.9degrees. how high is the rock?

75.25 m  to the nearest hundredth.

Step-by-step explanation:

We have 2 right angled triangles here  one  'inside ' the other.

Let the height of the rock be  x m and the distance of the rock from the first point be  y m . Then  the distance of the  second point from the rock = (y - 117) m.

Using trigonometry of the 2 triangles:

tan 19.4 = x/y

tan 37.9 = x / ( y - 117)

0.3522 = x/y               -  A.

0.7785 = x / ( y - 117)    - B.

From A:  x = 0.3522y

Substitute for x in B:

0.7785 =  0.3522y / (y - 117)

0.3522y = 0.7785y - 91.085

0.7785y - 0.3522y = 91.085

y = 91.085 / ( 0.7785-0.3522)

= 213.64 m

So the height x of the rock = 0.3522*213.664

= 75.25 m.

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