# A geologist measured a 40-degree angle of elevation to the top of a mountain. After moving 0.5m farther away, the angle of elevation was 34 degrees. How high is the top of the mountain?

1
by samfunte

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by samfunte

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which the opposite side is the height that we looking for.

and the adjacent side is the distance from his feet to the bottom of the mountain

let

and

at first situation measurement

tan (40) = h/d

and make d in terms of h

by algebra skills

d = h/tan (40)

at the second situation he move 0.5m farther so it will plus to the distance at the first situation

then it becomes

tan (34) = h/d +0.5

then manipulate the equation

you have the value of d at the first situation so just substitute the d

then it becomes

tan (34) = h / (h/tan40) + 0.5

then solve the

tan34 (h/tan40 + 0.5) =h

distribute the tan(34)

h tan34/tan40 + (0.5)tan34 = h

combine like terms

0.5(tan34) = h (1 - tan34/tan40 )

then you get the h

h = 0.5(tan34)/(1 - tan34/tan40 )

and tell your teacher that it is not mountain it is punso haha joke..

I hope it helps you !