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Exercises Trigonometry

Example 1 from Algebra and Trigonometry, 7.2 Right Triangle Trigonometry

Evaluating a Trigonometric Function of a Right Triangle

Given the triangle shown in Figure 3, find the value of $\cos α .$

A right triangle with side lengths of 8, 15, and 17. Angle alpha also labeled which is opposite to the side labeled 8.

Figure 3

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
The side adjacent to the angle is 15, and the hypotenuse of the triangle is 17.

$\begin{matrix} \cos (α) & = & \frac{adjacent}{hypotenuse} \\ = & \frac{15}{17} \end{matrix}$

Your turn

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

Given the triangle shown in Figure 4, find the value of $sin t .$

A right triangle with sides of 7, 24, and 25. Also labeled is angle t which is opposite the side labeled 7.

Figure 4

How did it go?

PreviousFinding a Linear Speed Next Evaluating Trigonometric Functions of Angles Not in Standard Position

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.