Geometry Notes Lesson 5.3C Trigonometry T.2.G.6 Use trigonometric ratios (sine, cosine, tangent) to determine lengths of sides and measures of angles in right triangles including angles of elevation and angles of depression T.2.G.7 Use similarity of right triangles to express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given lengths of sides

Solving for unknown values Steps: Label the sides as: opposite, adjacent, hypotenuse. Decide which trig ratio is needed: (sine, cosine, or tangent). Set up Equation Use Calculator to Solve.

We Will Work Backwards Since we know the ratio of the sides for every _______________, then we can find any angle, given 2 ___________of a right triangle.

Example #1 Find x. Round your answer to the nearest tenth. 18 xx 39

Example #2 Find x. Round your answer to the nearest tenth. 11 xx 15

Now You Try… Find x. Round your answer to the nearest tenth xx 41.7

Angle of Elevation/Depression Angle of Elevation: Angle of Depression: When a point is viewed from a lower point, the angle that person’s line of sight makes with the horizontal An angle that mopes around the house all day saying “I hate my life, nobody likes me.” JUST KIDDING! When a point is viewed from a higher point, the angle that person’s line of sight makes with the horizontal

Illustrations

Example #4 If state law requires playground slides to be placed at a 30 o angle of elevation and the slide is 10 feet long, how many feet are needed on the playground for the slide?

Steps 1.Draw a picture 2.Label the sides as opposite, adjacent, hypotenuse 3. Decide which Trig ratio is needed: (Sine, Cosine, Tangent) 4.Set up Equation 5.Use Calculator to solve.

Now You Try… A guy wire is attached to the top of a telephone pole. Its angle of depression with the horizontal is 76 o. If the pole is 20 feet tall, how long is the wire?