How high is the mountain

Question

How high is the mountain if Matt measures the angle of elevation of the peak of a mountain as 35º, and Susie, who is 1200 feet closer on a straight level path, measures the angle of elevation as 42º?

Answer 1

Using laws of sines

 

Consider two triangles

 

one with Susie at the base angle of 42 so third angle of the right angle triangle is 48

 

sin42/h = sin 48/n  -  h is height of mountain and n is distance of susie from mountain base

 

Other triangle with Matt at the base angle of 35 so third angle of the right angle triangle is 55

 

sin 35/h = sin 55/(n + 1200)

 

Solve these two equations and get the value of h

Answer 2

tan 42 ° = h/n

 

 

   Tan (35° ) = h/ ( 1200 +n)

 

     ntan 42° = ( 1200 +n)  tan 35°

 

    n ( tan 42- tan35) = 1200 tan 35=

 

     n = 1200tan 35/ ( tan42 - tan 35) = 4197.12

 

     tan 42= h/n

 

      h = n ( tan42) = 3779.1 

Answer 3

Tzipka,

This is a geometry problem with 2 unknowns.  Start by drawing it on paper.  The smaller triangle created by Susie, the ground, and the mountain will be labeled with the 2 unknowns: X and Y.  X extends from Susie to the base of the mountain and Y is the height of the mountain.  Put the known angle of 42º inside that triangle next to Susie.  Then draw the bigger triangle starting from where Matt stands.  The distance from Matt to the mountain is 1200+X.

 

So now you have 2 equations with 2 unknowns.  Do you see them?

 

Hint: you will use the tangent operator on each angle to be equal to the ratio of the height of the mountain to the distance from the person to the mountain base.