College Algebra & Trigonometry, 2018a

8.5. MORE APPLICATIONS 379
To solve this system of equations, we’ll set the first one equal to h:
tan 74 ◦ = h x
x ∗ tan 74 ◦ = h
Then, substitute this into the second equation:
tan 61 ◦ =
h
x+50
tan 61 ◦ x tan 74◦
=
x+50
Multiply on both sides by x +50:
(x + 50) tan 61 ◦ =
x tan 74◦
x+50
(x + 50)
So,
(x + 50) tan 61 ◦ = x tan 74 ◦
There are two options to solve this equation - we can hold on to the tangents
as they are and solve for x in terms tan 74 ◦ and tan 61 ◦ , or we can approximate
tan 74 ◦ and tan 61 ◦ and generate an approximate value for x and h. First we’ll
approximate:
(x + 50) tan 61 ◦ = x tan 74 ◦
(x + 50) ∗ 1.804 ≈ 3.4874x
1.804x +90.2024 ≈ 3.4874x
90.2024 ≈ 1.6834x