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Exercises Trigonometry

Example 2 from Algebra and Trigonometry, 10.2 Non-right Triangles: Law of Cosines

Solving for an Angle of a SSS Triangle

Find the angle $α$ for the given triangle if side $a = 20,$ side $b = 25,$ and side $c = 18.$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
For this example, we have no angles. We can solve for any angle using the Law of Cosines. To solve for angle $α,$ we have

$\begin{array}{l} a^{2} = b^{2} + c^{2} −2 b c \cos α \\ 20^{2} = 25^{2} + 18^{2} −2 (25) (18) \cos α & Substitute the appropriate measurements . \\ 400 = 625 + 324 - 900 \cos α & Simplify in each step . \\ 400 = 949 - 900 \cos α \\ −549 = −900 \cos α & Isolate cos α . \\ \frac{−549}{−900} = \cos α \\ 0.61 \approx \cos α \\ \cos^{−1} (0.61) \approx α & Find the inverse cosine . \\ α \approx 52.4° \end{array}$
See Figure 5.

Figure 5

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Given $a = 5, b = 7,$ and $c = 10,$ find the missing angles.

How did it go?

PreviousFinding the Unknown Side and Angles of a SAS Triangle Next Using the Law of Cosines to Solve a Communication Problem

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 10.2, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.