Solving Right Triangles 8-3 Solving Right Triangles Warm Up Lesson Presentation Lesson Quiz Holt Geometry

Warm Up Use ∆ABC for Exercises 1–3. 1. What side is opposite of B? 2. What side is adjacent to A? 3. What does tan A = ? 4. What side is the hypotenuse? 5. What does tan B = ?

Objective Find the sine and cosine of an acute angle. Use trigonometric ratios to find angle measures in right triangles and to solve real-world problems.

Vocabulary sine cosine

San Francisco, California, is famous for its steep streets San Francisco, California, is famous for its steep streets. The steepness of a road is often expressed as a percent grade. Filbert Street, the steepest street in San Francisco, has a 31.5% grade. This means the road rises 31.5 ft over a horizontal distance of 100 ft, which is equivalent to a 17.5° angle. You can use trigonometric ratios to change a percent grade to an angle measure.

Note 67

Example 1A: Finding Trigonometric Ratios Write the trigonometric ratio as a fraction. sin J

Example 1B: Finding Trigonometric Ratios Write the trigonometric ratio as a fraction. cos J

Check It Out! Example 1a Write the trigonometric ratio as a fraction. cos A

Check It Out! Example 1c Write the trigonometric ratio as a fraction. sin B

Example 3A: Calculating Trigonometric Ratios Use your calculator to find the trigonometric ratio. Round to the nearest hundredth. sin 52° Be sure your calculator is in degree mode, not radian mode. Caution! sin 52°  0.79

Example 3B: Calculating Trigonometric Ratios Use your calculator to find the trigonometric ratio. Round to the nearest hundredth. cos 19° cos 19°  0.95

Example 4B: Using Trigonometric Ratios to Find Lengths Find the length. Round to the nearest hundredth. QR

Example 4C: Using Trigonometric Ratios to Find Lengths Find the length. Round to the nearest hundredth. FD

Check It Out! Example 4b Find the length. Round to the nearest hundredth. ST

Check It Out! Example 2 Use your calculator to find each angle measure to the nearest degree. a. tan-1(0.71) b. cos-1(0.05) c. sin-1(0.67) tan-1(0.71)  35° cos-1(0.05)  87° sin-1(0.67)  42°

Example 3: Solving Right Triangles Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree.

Check It Out! Example 3 Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree.

Example 5: Travel Application A highway sign warns that a section of road ahead has a 7% grade. To the nearest degree, what angle does the road make with a horizontal line?

Exit Slip Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree. 1. 2. DF  5.7; mD  68°; mF  22° AC  0.63; BC  2.37; m B = 15°