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FOM 11 Practice Test Ch.4 – Trigonometry Name: ___________ Block: _____ Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1. Calculate sin 16° to four decimal places. Predict another term that equals sin 16°. a. –0.2756; sin 164° b. 0.2756; sin 164° c. 0.2756; –sin 16° d. none of the above ____ 2. Which law could you use to determine the unknown angle in this triangle? a. b. c. d. ____ the sine law only neither the sine law nor the cosine law the cosine law only the sine law and the cosine law 3. Determine the unknown side length to the nearest centimetre. a. b. c. d. 4.4 cm 4.3 cm 4.6 cm 4.7 cm ____ . In ∆FGH, GH = 4.5 cm and G = 15°. What is the height of the triangle from base GF? a. b. c. d. 1.5 cm 1.3 cm 1.2 cm 0.9 cm Short Answer . Write another term using the tangent ratio that is equivalent to tan 48°. . Determine the unknown side length to the nearest tenth of a centimetre. . Determine the unknown angle measure to the nearest degree. . Determine the unknown angle measure to the nearest degree. Problem . In ∆QRS, q = 1.7 m, r = 4.3 m, and s = 5.6 m. Solve ∆QRS by determining the measure of each angle to the nearest degree. Show your work and draw ∆QRS. 1. While golfing, Beth hits a tee shot from point T toward a hole at H. However, the ball veers 34° and lands at B. The scorecard says that H is 250 m from T. Beth walks 120 m to her ball. Sketch a diagram of this situation. How far, to the nearest metre, is her ball from the hole? Show your work. 1. A building is observed from two points (looking in the same direction), P and Q, that are 94.0 m apart. The angle of elevation is 42° at P and 33° at Q. Sketch the situation. Determine the height of the building to the nearest tenth of a metre. 1. An airplane is flying directly toward two forest fires. From the airplane, the angle of depression to one fire is 43° and 20° to the other fire. The airplane is flying at an altitude of 2500 ft. What is the distance between the two fires to the nearest foot? Show your work. FOM 11 Ch. 4 – Obtuse Triangle Trigonometry Practice Test Answer Section MULTIPLE CHOICE 1. 2. 3. 4. 5. 6. B C A A A C PROBLEM 5.62 = 1.72 + 4.32 – 2(1.7)(4.3)Cos S 9.98 = -14.62 Cos S -0.682… = Cos S 133.049 = S 133° = ∠S 12. SHORT ANSWER Find ∠R: 7. –tan 132° 8. Unknown Angle = 107° . . . ∠R = 34° ∠Q = 180° – ∠R – ∠S ∠Q = 13° x = 2.5 cm 9. Find Unknown Side: a2 = (2.7)2 + (4.9)2 – 2(2.7)(4.9)Cos116 a = 6.549755762… . .… Sin x = 0.3705… x = 21.747 x = 22° 10. 2.62 = 4.42 + 5.72 – 2(5.7)(4.4)Cos x -45.09 = -50.16Cos x 0.898… = Cos x 25.98 = x 26° = x 11. a is smaller than b Find h: h = bSinA = (7.5)Sin45 = 5.3 cm h<a<b ∴ two triangles: Find ∠B . ∠B = 62° or 118° 13. t2 = 1202 + 2502 – 2(120)(250) cos 34° t = 164.796... Beth's ball is 165 m from the hole. (180 – 62) 16. Draw a rough (not-to-scale) sketch of the situation, as shown. Determine the unknown angles using the property that the measures of the angles in a triangle sum to 180°. Let A and B represent the positions of the fires. 14. By the sine ratio 94.0 33 9 43 2500 +, BD = 3665.397… PR = 327.268… By the sine law, -+ 3665.397 … 23 20 Sin 42 = .!… AB = 4187.772 (327.268…)Sin 42 = 218.985 OR The height of the building is 219.0 m. tan 20 15. 2# tan 43 AC = 345 AC = 6868.694 # ∠C = 29.249 = 29° since Sin(x) = Sin(x – 180) OR ∠C = 180 – 29 = 151° ∠B = 180 – 29 – 20 = 131° OR OR Sine Law $ 350 sin 131 sin 20 b = 772.32 m BC = 345 BC = 2680.922 AB = AC – BC = 6868.694 – 2680.922 = 4187.772 The fires are 4188 ft apart. ∠B = 180 – 151 – 20 = 9° Cosine Law b2 = 5002 + 3502 – 2(500)(350)Cos 131 b = 775.96 m 2nd Triangle # Cosine Law b2 = 5002 + 3502 – 2(500)(350)Cos 9 b = 163.73 m OR Sine Law $ 350 sin 9 sin 20 b = 160.08