2. How do I use the sine, cosine, and tangent ratios to solve triangles?

3. Trigonometric Ratios A B C a b c 5.3Apply the Sine and Cosine Ratios

4. 5.3Apply the Sine and Cosine Ratios Sine and Cosine Ratios Let  ABC be a right triangle with acute The sine of and cosine of (written sin A and cos A) is defined as follows:

5. 5.3Apply the Sine and Cosine Ratios Example 1 Find sine ratios Find sin X and sin Y. Write each answer as a fraction and as a decimal rounded to four places.

6. 5.3Apply the Sine and Cosine Ratios Example 2 Find cosine ratios Find cos X and cos Y. Write each answer as a fraction and as a decimal rounded to four places.

7. 5.3Apply the Sine and Cosine Ratios Checkpoint. Find the indicated measure. Round to 4 decimal places, if necessary. 1.Find sin A and sin B. 2.Find cos A and cos B.

8. 5.3Apply the Sine and Cosine Ratios Example 3 Use trigonometric ratios to find side lengths Use a trigonometric ratio to find the value of x in the diagram. Round to the nearest tenth.

9. 5.3Apply the Sine and Cosine Ratios Example 3 Use trigonometric ratios to find side lengths Use a trigonometric ratio to find the value of x in the diagram. Round to the nearest tenth.

10. 5.3Apply the Sine and Cosine Ratios Find the sine and cosine of andof the similar triangles. Then compare the ratios. Example 4 Sine and cosine ratios for similar triangles

11. 5.3Apply the Sine and Cosine Ratios Example 4 Sine and cosine ratios for similar triangles Find the sine and cosine of andof the similar triangles. Then compare the ratios. In  XYZ, and are _______________ angles, so sin X = cos ___ and sin Y = cos ___. complementary Y X In  LMN, and are _______________ angles, so sin L = cos ___ and sin M = cos ___. complementary M L Because  XYZ and  LMN are _______ triangles, sin X = sin ___, cos X = cos ___, sin Y = sin ___, and cos Y = cos ___. similar L L M M

12. 5.3Apply the Sine and Cosine Ratios Example 5 Use trigonometric ratios to find side lengths Find the height of the parking ramp shown.

13. 5.3Apply the Sine and Cosine Ratios Checkpoint. Complete the following exercises. 3.Find the value of x. Round to the nearest tenth.

14. 5.3Apply the Sine and Cosine Ratios Checkpoint. Complete the following exercises. 4.Find the value of y. Round to the nearest tenth.

15. 5.3Apply the Sine and Cosine Ratios Pg. 180, 5.3 #1-19