Chapter 7 Test. 2. In triangle ABC, A = 60, and side c = 20 ft. How many triangles can be formed if side a = 16 ft? A) 0 B) 1 C) 2 D) 3

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1 Name Chapter 7 Test 1. Solve the triangle using the law of sines. Round to the nearest tenth. side a = 12 m A = 19 B = 79 What are the lengths of sides b and c? A) b = 35.5 m, c = 35.9 m C) b = 36.2 m, c = 36.5 m B) b = 36.0 m, c = 36.9 m D) b = 36.7 m, c = 36.3 m 2. In triangle ABC, A = 60, and side c = 20 ft. How man triangles can be formed if side a = 16 ft? A) 0 B) 1 C) 2 D) 3 3. Solve using the law of sines and a scaled drawing. If two triangles eist, solve both completel. Round to the nearest tenth. side a = 10.8 mi B = 55 side b = 9.0 mi A) A = 79.4, C = 45.6, c = 7.8 mi B) A = 100.6, C = 24.4, c = 4.5 mi C) A = 79.4, C = 45.6, c = 7.8 mi or A = 100.6, C = 24.4, c = 4.5 mi D) Not possible 4. Use the law of sines to determine if no triangle, one triangle, or two triangles can be formed from the diagram given (diagram ma not be to scale), then solve. If two solutions eist, solve both completel. Note the arrowhead marks the side of undetermined length. Round side to the nearest tenth and angles to the nearest whole number. 41 mm 44 mm A) one triangle: A 8, B 113, a 6.7 mm B) one triangle: A 54, B 67, a 38.7 mm C) two triangles: A 54, B 67, a 38.7 mm or A 8, B 113, a 6.7 mm D) not possible

2 5. A blimp is moored at a hangar near an airport. From an unknown distance awa, the angle of elevation is measured at After moving 130 d closer, the angle of elevation has become At what height is the blimp moored? Round to the nearest tenth. A) d B) d C) d D) d 6. Determine whether the law of sines can be used to begin the solution process for the triangle. A 8 cm 11 cm C 13 cm (figure not drawn to scale) A) Yes B) No 7. Solve for the unknown part. Round to the nearest tenth. 6 2 = (10)(12)cos B A) B = 29.4 B) B = 29.6 C) B = 29.9 D) B = Solve triangle ABC using the law of cosines. Round to the nearest tenth in (figure not to scale) A) B = 35.8, C = 61.2, a = 13.6 in C) B = 35.8, C = 61.2, a = 6.2 in B) B = 68.2, C = 28.8, a = 13.6 in D) B = 68.2, C = 28.8, a = 6.2 in Copright 2011, McGraw Hill, Coburn Trig 2e Page 2

3 9. A pilot wishes to fl from Pleasant Hills to Sheldon. She calculates the distances shown using a map, with York for reference since it is due west from Pleasant Hills. What heading should she set for this trip (i.e., what is the measure of angle P)? Round to the nearest tenth. S Sheldon 119 miles 852 miles Y York 759 miles (figure not drawn to scale) A) 4.4 B) 5.3 C) 6.5 D) 7.2 Pleasant Hills P 10. Find the equivalent position vector for vector v with initial point (4, 2) and terminal point (3, 3). A) 7, 5 B) 7, 1 C) 1, 1 D) 1,1 Use the following to answer questions 11-12: Vector v = 1,6 has initial point (2, 5). 11. Find the terminal point of the vector. A) (3, 11) B) ( 1, 1) C) (1, 1) D) (3, 1) 12. Find the magnitude of the vector. A) 29 B) 37 C) 29 D) The magnitude of vector v is given, along with the quadrant of the terminal point and the angle it makes with the nearest -ais. Find the horizontal and vertical components of v, rounded to one decimal place, and write the result in component form. v = 26, θ = 66, QIII A) v = 23.8, 10.6 C) v = 10.6, 23.8 B) v = 10.6, 23.8 D) v = 23.8,10.6 Copright 2011, McGraw Hill, Coburn Trig 2e Page 3

4 Use the following to answer questions 14-15: u = 3, 4 ; v = 1,3 14. Compute 5u + 2v. A) 13, 26 B) 12, 26 C) 13, 25 D) 12, Compute u 3v. A) 6, 6 B) 5, 5 C) 6, 5 D) 5, For the vectors u and v shown, compute and u v and represent each result graphicall. 5 (-1, 2) (2, 1) v u -5 5 A) C) 5 u - v u - v 5-5 B) D) 5 u - v u - v 5-5 Copright 2011, McGraw Hill, Coburn Trig 2e Page 4

5 17. For the vector below, θ represents the acute angle formed b the vector and the -ais. Write the vector in i, j form. Round to the nearest tenth. v in QIV, v = 27, θ = 76 A) v = 26.2i + 6.5j C) v = 6.5i j B) v = 26.2i 6.5j D) v = 6.5i 26.2j 18. Three cowhands have roped a wild stallion and are attempting to hold him stead. The first and second cowhands are pulling with the magnitude and at the angles indicated in the diagram. If the stallion is held fast b the three cowhands, find the magnitude and angle of the rope from the third cowhand. Round the magnitude to the nearest hundredth and the angle to the nearest tenth. F 1 F o?f 3 73 o A) F ; θ C) F ; θ B) F ; θ D) F ; θ A 325-kg carton is sitting on a ramp, held stationar b 250 kg of tension in a restraining rope. Find the ramp's angle of incline to the nearest tenth of a degree. 250 kg (figure not to scale) A) 50.3 B) 39.7 C) 39.9 D) 41.2 Use the following to answer questions 20-21: p = 1,5 ; q = 2, 2 Copright 2011, McGraw Hill, Coburn Trig 2e Page 5

6 20. Compute the dot product p q. A) 2, 10 B) 5, 4 C) 8 D) Find the angle between the vectors to the nearest tenth of a degree. A) B) C) D) Find comp v u. Round to the nearest hundredth. u = 7,8, v = 1,7 A) 4.61 B) 8.91 C) 5.93 D) 6.93 Use the following to answer questions 23-24: u = 1,5 ; v = 4, Find the projection of u along v (compute proj v u). Round to the nearest hundredth, if necessar. A) 1.18, 5.88 B) 0.23, 1.15 C) 1.2,0.6 D) 5.37, Resolve u into vectors u 1 and u 2 where u 1 v and u 2 v. Round to the nearest hundredth, if necessar. A) u 1 = 0.23,1.15, u 2 = 1.23,6.15 C) u 1 = 1.2,0.6, u 2 = 0.2,5.6 B) u 1 = 0.23,1.15, u 2 = 0.77,3.85 D) u 1 = 1.2,0.6, u 2 = 2.2, 4.4 Copright 2011, McGraw Hill, Coburn Trig 2e Page 6