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Maths Quest 11 Maths B for Queensland WorkSHEET 4.2 1 Chapter 4 Triangle Trigonometry WorkSHEET 4.2 Triangle Trigonometry Find the unknown marked sides correct to 2 decimal places. 1 Name: ___________________________ tan 37° = 10 x 4 10 tan 37 x = 1327 (correct to 2 decimal places) 10 sin 37° = h 10 h = sin 37 h = 16.62 (correct to 2 decimal places) x= 2 Find the value of . 10 8 tan 1.25 tan 2 51.3 3 From a vertical fire tower 50 m high, the angle of depression is 4° to a fire. How far away is the fire to the nearest metre is the fire? 3 tan 4 h 50 d 50 tan 4 h 715 m (to the nearest metre) Maths Quest 11 Maths B for Queensland 4 Chapter 4 Triangle Trigonometry WorkSHEET 4.2 A person 1.6 m tall stands 30 m from a building and measures the angle of elevation to the top of the building as 48°. How high is the building to the nearest metre? 2 3 h 30 h = 30 tan 48° h = 333 m Height of building = 33.3 1.6 m = 34.9 = 35 m (to the nearest metre) tan 48° = 5 In triangle ABC, a = 8, c = 12, and C = 52°. Find A. 3 sin A sin 52 8 12 8 sin 52 12 sin A 0.5253 sin A A 31.7 6 Find the value of length x correct to 1 decimal place. x sin 57 x 8 sin 62 8 sin 57 sin 62 x 7.6 (correct t o 1 decimal place) 3 Maths Quest 11 Maths B for Queensland 7 Chapter 4 Triangle Trigonometry WorkSHEET 4.2 Consider the figure drawn below. (a) ADB 40 a b sin A sin B BD 50 sin 20 sin 40 BD (a) Find an expression for the length BD. (b) Find h correct to 1 decimal place. (b) 3 50 sin 20 sin 40 opp hyp h sin 60 BD sin h BD sin 60 50 sin 20 sin 60 sin 40 23.0 8 Find the third side of the triangle ABC, given a = 8, c = 12 and B = 75°. State your answer correct to 2 decimal places. 9 Find the smallest angle in the triangle with sides 5, 8 and 10. b2 = 82 122 (2 8 12 cos 75°) = 64 144 49.69 = 158.31 b = 158.31 = 12.58 (correct to 2 decimal places) 3 8 2 10 2 5 2 2 8 10 139 cos 160 cos 0.8688 3 cos 29.7 Maths Quest 11 Maths B for Queensland 10 Chapter 4 Triangle Trigonometry WorkSHEET 4.2 A triangle has sides 6 cm, 7 cm and 9 cm. Find the size of the largest angle correct to the nearest minute. Largest side lies opposite the largest angle. b2 c2 a2 cos A 2bc cos 62 72 92 267 36 49 81 84 4 84 4 cos 1 84 87 16 4