LT 8.2: Use Trig ratios to find side lengths in right triangles and to solve real-world problems.

Vocabulary Trigonometric ratio is a ratio of two sides of a right triangle.

Math Humor Q: What happened to the geometry student who went to the beach to catch some rays? A: He became a tangent!

S Oppos Hypo t enuse Cos i ne Ad j acen t Hypo t enuse Tangen t Oppos I t e Ad j acen t

Example 1: Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.

Example 2 Use a special right triangle to write each trigonometric ratio as a fraction. sin 60˚ sin 45˚ cos 60˚ tan 45˚ tan 60˚

Example 3 Use your calculator to find the trigonometric ratio. Round four places. cos 30° sin 62° tan 11°

Example 4 Find the length of DF. Round to the nearest hundredth.

Example 5 Find the length of ST. Round to the nearest hundredth.

Example 6 Find the length BC. Round to the nearest hundredth.

Example 8 The Pilatusbahn in Switzerland is the world’s steepest cog railway. Its steepest section makes an angle of about 25.6º with the horizontal and rises about 0.9 km. To the nearest hundredth of a kilometer, how long is this section of the railway track? 0.9 km