Trigonometry

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1. What is the area of triangle ABC if a = 47.0°, β = 57.8°, and a = 10.2 cm?

A. 58.2 cm2
B. 43.5 cm2
C. 38.4 cm2
D. 33.3 cm2

2. Given triangle ABC with β = 41°, g = 14°, and a = 5.0, find the value of c.

A. 6.2
B. 4.0
C. 1.5
D. 17

3. Resolve the vector, v, with magnitude 2.0 × 102 and angle 60°.

A. v = 170i + 100j
B. v = 120i + 160j
C. v = 100i + 170j
D. v = 10i + 17j


4. What is the area of triangle ABC if a = 83.4 ft, b = 53.1 ft, and c = 37.2 ft?

A. 16,100 ft2
B. 709 ft2
C. 1,220 ft2
D. 76.0 ft2

5. Which of the following statements relating to the Pythagorean theorem are true?
(i) The magnitude of a vector is based on the Pythagorean theorem.

(ii) The law of cosines is based on the Pythagorean theorem.

(iii) The law of sines is based on the Pythagorean theorem.

A. (i) and (ii)
B. (i) only
C. (ii) only
D. (ii) and (iii)

6. How much work is done by raising a 117-lb box vertically 18.0 inches?

A. 25,300 ft-lb
B. 2,110 ft-lb
C. 176 ft-lb
D. 5,190 ft-lb

7. Given triangle ABC with g = 61.0°, β = 29.0°, and b = 20.5, find the value of a.

A. 37.0
B. 11.4
C. 42.3
D. 9.94

8. Given triangle ABC with b = 14.0, c = 11.0, and β = 105°, find the value of a.

A. 20
B. 8.7 and 20
C. 6.3
D. 6.3 and 12

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