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Chapter 7 Measurement 7.4 MATHPOWERTM 10, WESTERN EDITION 7.4.1 Adjacent Opposite Opposite The Primary Trigonometric Ratios Hypotenuse q Hypotenuse q Adjacent Sine q = Opposite Hypotenuse Adjacent Cosine q = Hypotenuse Opposite Tan q = Opposite Adjacent Soh Cah Toa QuickTi me™ and a GIF decompressor are needed to see thi s pi ctur e. 7.4.2 Determining Values of Primary Trigonometric Ratios 12 5 13 13 5 13 12 13 12 5 15 5 12 25 20 25 20 15 25 25 15 20 20 15 7.4.3 Trigonometric Ratios of Acute Angles Find each of the following, to three decimal places: a) sin 640 = 0.899 d) tan 140 = 0.249 b) cos 280 = 0.883 e) sin 590 = 0.857 c) tan 480 = 1.111 f) cos 820 = 0.139 Find the measure of each angle, to the nearest degree: 0 0 d) tan A = 0.7563 37 19 a) sin A = 0.3214 b) cos B = 0.6541 490 e) sin B = 0.5421 c) tan C = 1.2312 510 f) cos C = 2 330 undefined 7.4.4 Finding the Length of an Unknown Side opp Tanq = adj x Tan 34 = 16 Quic kTime™ and a GIF decompressor are needed to see this picture . x = 16 Tan 34 x = 10.8 cm adj cosq = hyp 16 cos 34 = y 16 y= cos 34 QuickTime™ and a GIF decompressor are needed to see this picture. opp sinq = hyp x sin42 = 27 x = 27 sin42 x = 18.1 cm Quic kTime™ and a GIF decompressor are needed to see this picture . y = 19.3 cm adj cosq = hyp y cos 42 = 27 y = 27 cos42 y = 20.1 cm 7.4.5 Find the Measure of the Unknown Angle c2 = a2 + b2 262 = x2 + 192 x2 = 262 - 192 x2 = 315 x = 17.7 cm adj cosq = hyp 19 cos q = 26 q = 43.00 QuickTime™ and a GIF decompressor are needed to see this picture. c2 = a2 + b2 x2 = 142 + 222 x2 = 680 x = 26.1 cm opp tanq = adj 14 tan q = 22 q = 32.50 7.4.6 Solving a Right Triangle To solve a right angle triangle means to find all missing sides and angles. A 0 510 x y C 26 sin 51 = x 26 x= 0 sin 51 B x = 33.5 cm 26 tan 51 = y 0 26 cm B = 180 0 (90 0 510 ) B = 390 Quic kTime™ anda GIFdec ompres sor areneededtoseethis picture. 26 y= 0 tan 51 y = 21.1 cm AB = 33.5 cm AC = 21.1 cm B = 390 7.4.7 Solving Problems Involving Trigonometry- Problem 1 A tree casts a shadow 12 m long. The angle to the top of the tree from the end of the shadow is 680. Find the height of the tree. opp Tanq = adj x Tan68 = 12 x = 12 sin 68 x = 11.13 m The tree is 11.13 m tall. 7.4.8 Solving Problems Involving Trigonometry- Problem 2 A 12 m ladder is leaned up against a brick wall. If the ladder forms an angle of 360 with the wall, find the height of the wall. 360 12 m x opp Cosq = hyp x 0 Cos36 = 12 x = 12 cos360 x = 9.71 m The wall is 9.71 m high. 7.4.9 Solving Problems Involving Trigonometry- Problem 3 Find the height of the cliff. y cos50 = 70 0 y = 70 cos500 y = 45.0 m x x Tan40 = 45 0 y x = 45 Tan400 x = 37.76 m The cliff is 37.76 m high. 7.4.10 Suggested Questions: Page 329 4 1, 2 5 1-6 6 1-6 Page 332 1, 2, 6, 8 - 14, 17