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Exercises Trigonometry

Example 4 from Algebra and Trigonometry, 10.1 Non-right Triangles: Law of Sines

Finding the Triangles That Meet the Given Criteria

Find all possible triangles if one side has length 4 opposite an angle of 50°, and a second side has length 10.

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
Using the given information, we can solve for the angle opposite the side of length 10. See Figure 14.

$\sin^{- 1} (1.915)$

Figure 14

We can stop here without finding the value of $α .$ Because the range of the sine function is $[- 1, 1],$ it is impossible for the sine value to be 1.915. In fact, inputting $\sin^{- 1} (1.915)$ in a graphing calculator generates an ERROR DOMAIN. Therefore, no triangles can be drawn with the provided dimensions.

Your turn

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

Determine the number of triangles possible given $a = 31,$ $b = 26,$ $β = 48° .$

How did it go?

PreviousSolving for the Unknown Sides and Angles of a SSA Triangle Next Finding the Area of an Oblique Triangle

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 10.1, 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.