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Exercises Trigonometry

Example 5 from Algebra and Trigonometry, 7.2 Right Triangle Trigonometry

Finding Missing Side Lengths Using Trigonometric Ratios

Find the unknown sides of the triangle in Figure 11.

A right triangle with sides a, c, and 7. Angle of 30 degrees is also labeled which is opposite the side labeled 7.

Figure 11

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
We know the angle and the opposite side, so we can use the tangent to find the adjacent side.

$\tan (30°) = \frac{7}{a}$
We rearrange to solve for $a .$

$\begin{matrix} a & = & \frac{7}{\tan (30°)} \\ \approx & 12.1 \end{matrix}$
We can use the sine to find the hypotenuse.

$\sin (30°) = \frac{7}{c}$

Again, we rearrange to solve for $c .$

$\begin{matrix} c & = & \frac{7}{\sin (30°)} \\ = & 14 \end{matrix}$

Your turn

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

A right triangle has one angle of $\frac{π}{3}$ and a hypotenuse of 20. Find the unknown sides and angle of the triangle.

How did it go?

PreviousUsing Cofunction Identities Next Measuring a Distance Indirectly

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 7.2, 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.