Reviewing Trig Ratios 7.4 Chapter 7 Measurement 7.4.1 MATHPOWERTM 10, WESTERN EDITION 7.4.1

Soh Cah Toa The Primary Trigonometric Ratios q Hypotenuse Hypotenuse Opposite Opposite Opposite Opposite Opposite Adjacent q Adjacent Adjacent Adjacent Adjacent Opposite Opposite Hypotenuse Opposite Adjacent Sine q = Tan q = Soh Cah Toa Adjacent Hypotenuse Cosine q = 7.4.2

Determining Values of Primary Trigonometric Ratios 7.4.3

Trigonometric Ratios of Acute Angles Find each of the following, to three decimal places: a) sin 640 = b) cos 280 = c) tan 480 = 0.899 d) tan 140 = e) sin 590 = f) cos 820 = 0.249 0.857 0.883 1.111 0.139 Find the measure of each angle, to the nearest degree: 190 d) tan A = 0.7563 e) sin B = 0.5421 f) cos C = 2 370 a) sin A = 0.3214 b) cos B = 0.6541 c) tan C = 1.2312 330 490 510 undefined 7.4.4

Finding the Length of an Unknown Side x = 16 Tan 34 x = 10.8 cm y = 19.3 cm x = 27 sin42 x = 18.1 cm 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 q = 43.00 c2 = a2 + b2 x2 = 142 + 222 x2 = 680 x = 26.1 cm 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 510 x y x = 33.5 cm y = 21.1 cm B C 26 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. 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 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 = 70 cos500 y = 45.0 m x 45 x = 45 Tan400 x = 37.76 m y The cliff is 37.76 m high. 7.4.10

Assignment Suggested Questions: Page 329 Page 332 4 1, 2 4 1, 2 5 1 - 6 6 1 - 6 Page 332 1, 2, 6, 8 - 14, 17