College Algebra & Trigonometry, 2018a

378 CHAPTER 8. RIGHT TRIANGLE TRIGONOMETRY
8.5 More Applications
Sometimes solving problems involving right triangles requires the use of a system
of equations. A common method for determining the height of an object
whose base is inaccessible is that of measuring the angle of elevation from two
different places in front of the object. If you measure the angle of elevation to the
top of of a radio antenna as 74 ◦ , then walk back 50 feet and measure the angle of
elevation to the top of the antenna as 61 ◦ , then we would have something like the
diagram below:
61 ◦
50 ft.
74 ◦
One of the first things we can do is introduce some labels for the unknown distances:
h
61 ◦
50 ft.
74 ◦
x
Then, we can say that:
tan 74 ◦ = h x
tan 61 ◦ =
h
x+50