College Algebra & Trigonometry, 2018a

360 CHAPTER 8. RIGHT TRIANGLE TRIGONOMETRY
Example 1
Solve the triangle. Round side lengths to the nearest 100 th and angles to the nearest
10 th of a degree.
α
8
5
θ
We can find the third side of the triangle by using the Pythagorean Theorem.
a 2 +5 2 =8 2
a 2 +25=64
a 2 =39
a = √ 39 ≈ 6.24
When solving problems of this type, I encourage people to use the most accurate
values that are available in the problem. This way, there is less chance for
rounding error to occur.
If we take the values for the sides that were given in the problem (5 and 8), then
we can say that
cos θ = 5 8
θ =cos −1 ( 5 8 )
θ ≈ 51.3 ◦
Then α would be 90 ◦ − 51.3 ◦ =38.7 ◦ ≈ α.