Driving across a flat area.The angle of elevation to the peak is 4 degrees.13 miles closer to the mountain, the angle of elevation is 10 degrees. How tall?

Question

Precalculus

How tall is the mountain?**

Answer 1

I will set up a solution for you, and then you take it from there.  First, try drawing a diagram of the situation.  Let x be the distance from the second position to the mountain, and let h be the height of the mountain.  From the diagram you should be able to see that

 

h/(13 + x) = tan4°

 

h/x = tan10º

 

You have a system of 2 equations in 2 unknowns h and x.  Now try to solve for h and x by elimination and finish from here.