Use Right-Triangle Relationships

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Identify the hypotenuse, opposite the right angle. For legs a and b, a^2 + b^2 = c^2. Relative to an acute angle, sine is opposite/hypotenuse and cosine is adjacent/hypotenuse.

Worked example

A right triangle with legs 9 and 12 has hypotenuse sqrt(81 + 144) = 15. For the angle opposite the side of length 9, sine is 9/15 = 3/5.

1. A right triangle has legs 5 and 12. What is its hypotenuse? Answer

2. A right triangle has hypotenuse 10 and one leg 6. What is the other leg? Answer

3. An acute angle has opposite side 8 and hypotenuse 17. What is its sine? 17/8 8/17 8/15

4. An acute angle has adjacent side 12 and hypotenuse 13. What is its cosine? 12/13 5/13 13/12

5. Can side lengths 6, 8, and 11 form a right triangle? Yes, because 6 + 8 is greater than 11 Yes, because 11 is the longest side No: 6^2 + 8^2 does not equal 11^2