Instructions: Show all required work! NO WORK = NO MARKS!!!!!! 1. Sketch a triangle that corresponds to the equation. (1 mark) Then, determine the third angle measure. (1 mark) Sketch: Measure of third angle: 2. Determine the length of c to the nearest tenth of a centimetre. (2 marks) 3. Determine the length of d to the nearest tenth of a centimetre. (2 marks)
4. Determine the measure of to the nearest degree. (2 marks) 5. In GHI, G = 36, g = 20.4 cm, and H = 72. Draw the diagram of the triangle. (1 mark) Determine the length of side h to the nearest tenth of a centimetre. (2 marks) 6. In WXY, the values of w, x, and y are known. Write the form of the cosine law you could use to solve for the angle opposite w. (1 mark) 7. Determine the length of w to the nearest tenth of a centimetre. (2 marks)
8. Determine the measure of to the nearest degree. (2 marks) 9. In GHI, g = 30.0 cm, i = 19.3 cm, and H = 53. Draw the diagram of the triangle. (1 mark) Determine the measure of h to the nearest tenth of a centimetre. (2 marks)
10. A kayak leaves a dock on Lake Athabasca, and heads due north for 2.8 km. At the same time, a second kayak travels in a direction N70 E from the dock for 3.0 km. Draw a diagram and determine the distance between the kayaks, to the nearest tenth of a kilometre. (4 marks) 11. A radar operator on a ship discovers a large sunken vessel lying parallel to the ocean surface, 180 m directly below the ship. The length of the vessel is a clue to which wreck has been found. The radar operator measures the angles of depression to the front and back of the sunken vessel to be 52 and 67. How long, to the nearest tenth of a metre, is the sunken vessel? Draw a diagram and solve. (4 marks)
12. In TUV, U = 60, u = 8.7 m, and v = 7.6 cm. Solve the triangle. Round angles to the nearest degree and sides to the nearest tenth of a metre. Show your work. (6 marks) 13. Two airplanes leave Dawson City Airport at the same time. One airplane travels at 420 km/h. The other airplane travels at 375 km/h. About 2 h later, they are 1000 km apart. Determine the angle between their paths, to the nearest degree. Draw a diagram and solve. (4 marks)
FOM 11 Chapter 3 Test 2015 Answer Section SHORT ANSWER 1. ANS: 70, 18.8 PTS: 1 DIF: Grade 11 REF: Lesson 3.1 OBJ: 3.1 Draw a diagram to represent a problem that involves the cosine law or the sine law. 3.5 Solve a problem involving the sine law that requires the manipulation of a formula. TOP: Side-angle relationships in acute triangles 2. ANS: c = 42.7 cm KEY: primary trigonometric ratios OBJ: 3.5 Solve a problem involving the sine law that requires the manipulation of a formula. TOP: Proving and applying the sine law KEY: sine law 3. ANS: d = 6.2 cm OBJ: 3.5 Solve a problem involving the sine law that requires the manipulation of a formula. TOP: Proving and applying the sine law KEY: sine law 4. ANS: = 57 OBJ: 3.5 Solve a problem involving the sine law that requires the manipulation of a formula. TOP: Proving and applying the sine law KEY: sine law 5. ANS: h = 33.0 cm OBJ: 3.5 Solve a problem involving the sine law that requires the manipulation of a formula. TOP: Proving and applying the sine law KEY: sine law 6. ANS:
cos W = OBJ: 3.1 Draw a diagram to represent a problem that involves the cosine law or the sine law. 3.2 Explain the steps in a given proof of the sine law or cosine law. 7. ANS: w = 27.3 cm OBJ: 3.3 Solve a problem involving the cosine law that requires the manipulation of a formula. 8. ANS: = 57 OBJ: 3.3 Solve a problem involving the cosine law that requires the manipulation of a formula. 9. ANS: h = 24.0 cm OBJ: 3.3 Solve a problem involving the cosine law that requires the manipulation of a formula. 10. ANS: 3.3 km PTS: 1 DIF: Grade 11 REF: Lesson 3.4 OBJ: 3.1 Draw a diagram to represent a problem that involves the cosine law or the sine law. 3.6 Solve a contextual problem that involves the cosine law or sine law. TOP: Solving problems using acute triangles 11. ANS: 217.0 m PTS: 1 DIF: Grade 11 REF: Lesson 3.4 OBJ: 3.1 Draw a diagram to represent a problem that involves the cosine law or the sine law. 3.5 Solve a problem involving the sine law that requires the manipulation of a formula. 3.6 Solve a contextual problem that involves the cosine law or sine law. TOP: Solving problems using acute triangles KEY: sine law primary trigonometric ratios PROBLEM 12. ANS:
The measure of V is 49. T + U + V = 180 T + 60 + 49 = 180 T = 71 The length of t is 9.5 m. OBJ: 3.1 Draw a diagram to represent a problem that involves the cosine law or the sine law. 3.5 Solve a problem involving the sine law that requires the manipulation of a formula. 3.6 Solve a contextual problem that involves the cosine law or sine law. TOP: Proving and applying the sine law KEY: sine law 13. ANS: After 2 h, the plane travelling at 375 km/h has gone 750 km and the plane travelling at 420 km/h has gone 840 km. In a triangle that models the information, the unknown angle, is opposite the 1000 km side. 1000 2 = 750 2 + 840 2 2(750)(840) cos 1 000 000 = 562 500 + 705 600 1 260 000 cos 268 100 = 1 260 000 cos = cos = cos 1 (0.2127...) = 77.714... The angle between the two airplanes is 78. OBJ: 3.1 Draw a diagram to represent a problem that involves the cosine law or the sine law. 3.3 Solve a
problem involving the cosine law that requires the manipulation of a formula. 3.6 Solve a contextual problem that involves the cosine law or sine law.