College Algebra & Trigonometry, 2018a

380 CHAPTER 8. RIGHT TRIANGLE TRIGONOMETRY
53.58 ≈ x
x ∗ tan 74 ◦ = h
53.58 ∗ tan 74 ◦ ≈ h
186.87 feet ≈ h
The other method is a little tricky algebraically:
(x + 50) tan 61 ◦ = x tan 74 ◦
x tan 61 ◦ + 50 tan 61 ◦ = x tan 74 ◦
50 tan 61 ◦ = x tan 74 ◦ − x tan 61 ◦
50 tan 61 ◦ = x(tan 74 ◦ − tan 61 ◦ )
50 tan 61 ◦
(tan 74 ◦ −tan 61 ◦ ) = x
At this point, you can approximate the value of x and solve for h, or express the
value of h exactly as
tan 74 ◦ 50 tan 61
∗
◦
(tan 74 ◦ −tan 61 ◦ ) = h