Solving Right Triangles

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Presentation transcript:

Solving Right Triangles 8.3

Example 1: Identifying Angles from Trigonometric Ratios Use the trigonometric ratio to determine which angle of the triangle is A. Cosine is the ratio of the adjacent leg to the hypotenuse. The leg adjacent to 1 is 1.4. The hypotenuse is 5. The leg adjacent to 2 is 4.8. The hypotenuse is 5. Since cos A = cos2, 2 is A.

When you are finding an angle measurement, you must use the inverse keys on your calculator.

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) tan-1(0.75)  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. By thePythagorean Theorem, RT2 = RS2 + ST2 (5.7)2 = 52 + ST2 Since the acute angles of a right triangle are complementary, mT  90° – 29°  61°.

Example 4 Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree.

Example 5 Find the unknown measures. Round lengths to the nearest hundredth and angle measures to the nearest degree. Since the acute angles of a right triangle are complementary, mD = 90° – 58° = 32°. , so EF = 14 tan 32°. EF  8.75 DF2 = ED2 + EF2 DF2 = 142 + 8.752 DF  16.51