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Tuesday, February 19, 2013

Angle - Elevation Problem

Category: Trigonometry, Plane Geometry, Algebra

"Published in Newark, California, USA"

A tower of height h stands on level ground and is due north of point A and due east of point B. At A and B, the angles of elevation of the top of the tower are α and β, respectively. If the distance AB is c, show that 




Photo by Math Principles in Everyday Life

Solution:

In the given figure above, there are three right triangles involved. Let's solve for the height h in terms of α, β, and c as follows









By Pythagorean Theorem









Take the square root on both sides of the equation, we have



Therefore,