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8-4 Trigonometry, day 2 You used the Pythagorean Theorem to find missing lengths in right triangles. β’ Find trigonometric ratios using right triangles. β’ Use trigonometric ratios to find angle measures in right triangles. You can use a calculator to find the measure of an angle which is the inverse of the trigonometric ratio (sine, cosine, or tangent of an acute angle). p. 571 Inverse Trigonometric Ratios The expression π ππβ1 π₯ is read the inverse sine of x and is interpreted as the angle with sine x. Use the thought: If the tan 30°β.058, then tanβ1 0.58 β 30° Use a calculator to find the measure of οP to the nearest tenth. The measures given are those of the leg adjacent to οP and the hypotenuse, so write the equation using the cosine ratio. KEYSTROKES: 2nd [COS] ( 13 ÷ 19 ) Answer: ENTER 46.82644889 So, the measure of οP is approximately 46.8°. Use a calculator to find the measure of οD to the nearest tenth. A. 44.1° B. 48.3° C. 55.4° D. 57.2° Solve the right triangle. Round side measures to the nearest hundredth and angle measures to the nearest degree. Step 1 Find mοA by using a tangent ratio. Definition of inverse tangent 29.7448813 β mοA Use a calculator. So, the measure of οA is about 30ο°. Step 2 Find mοB using complementary angles. mοA + mοB =90 30 + mοB β 90 mοB β 60 Definition of complementary angles mοA β 30 Subtract 30 from each side. So, the measure of οB is about 60ο°. Step 3 Find AB by using the Pythagorean Theorem. (AC)2 + (BC)2 = (AB)2 Pythagorean Theorem 72 + 42 = (AB)2 Substitution 65 = (AB)2 Simplify. Take the positive square root of each side. 8.06 β AB Use a calculator. So, the measure of AB is about 8.06. Answer: mοA β 30, mοB β 60, AB β 8.06 Solve the right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree. A. mοA = 36°, mοB = 54°, AB = 13.6 B. mοA = 54°, mοB = 36°, AB = 13.6 C. mοA = 36°, mοB = 54°, AB = 16.3 D. mοA = 54°, mοB = 36°, AB = 16.3 8-4 Assignment day 2 Page 573, 12-15, 36-39, 42-44