9.6: SOLVING RIGHT TRIANGLES

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Presentation transcript:

9.6: SOLVING RIGHT TRIANGLES Inverse Trigonometric Functions

In Lesson 9-5, you learned that sin 30° = 0. 5 In Lesson 9-5, you learned that sin 30° = 0.5. Conversely, if you know that the sine of an acute angle is 0.5, you can conclude that the angle measures 30°. This is written as sin-1(0.5) = 30°.

Example 2: Calculating Angle Measures from Trigonometric Ratios Use your calculator to find each angle measure to the nearest degree. A. cos-1(0.87) B. sin-1(0.85) C. tan-1(0.71) cos-1(0.87)  30° sin-1(0.85)  58° tan-1(0.71)  35°

Check It Out! Example 2 Use your calculator to find each angle measure to the nearest degree. a. tan-1(0.75) b. cos-1(0.05) c. sin-1(0.67)

Example 6: Solving a Right Triangle in the Coordinate Plane The coordinates of the vertices of ∆PQR are P(–3, 3), Q(2, 3), and R(–3, –4). Find the side lengths to the nearest hundredth and the angle measures to the nearest degree.

Step 1 Find the side lengths. Plot points P, Q, and R. Example 6 Continued Step 1 Find the side lengths. Plot points P, Q, and R. PR = 7 PQ = 5 Y By the Distance Formula, P Q X R

Step 2 Find the angle measures. Example 6 Continued Step 2 Find the angle measures. P Q R Y X mP = 90° The acute s of a rt. ∆ are comp. mR  90° – 54°  36°

Lesson Quiz: Use your calculator to find each angle measure to the nearest degree. 1. cos-1 (0.97) 2. tan-1 (2) 3. sin-1 (0.59) Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree. 4. 5.