College Algebra & Trigonometry, 2018a

8.3. SOLVING TRIANGLES 361
Example 2
Solve the triangle. Round side lengths to the nearest 100 th and angles to the nearest
10 th of a degree.
5
68 ◦
First, we can find the other angle in the right triangle: 90 ◦ − 68 ◦ =22 ◦ .
Next, to find the sides, we choose a trigonometric ratio for which we know one
of the sides. In this problem, we can use either the sine or the cosine.
sin 68 ◦ = a 5
Approximating sin 68 ◦ on a calculator:
0.9272 ≈ a 5
5 ∗ 0.9272 ≈ a
4.6 ≈ a
When approximating a trigonometric value from the calculator, it is important to
use at least 4 decimal places of accuracy. Again, this is to avoid rounding errors.
To solve for the remaining side we can either use the Pythagorean Theorem or
use the method demonstrated above, but with the cos 68 ◦ .