Trigonometry Laws of Sines and Cosines 4

Question 1

What is the area of triangle ABC when a = 9, b = 12, and angle C = 50°?

Accepted Answer

Area = ½·9·12·sin 50°

Answer

Area = ½·9·12·cos 50°

Answer

Area = 9·12·sin 50°

Answer

Area = ½·(9 + 12)·sin 50°

Question 2

In triangle DEF, d = 7, e = 24, f = 25. Is this triangle a right triangle? What confirms this?

Accepted Answer

Yes, because the Law of Cosines gives cos F = 0

Answer

No, because 7² + 24² ≠ 25²

Answer

Yes, because 7² + 24² = 25² (Pythagorean triple)

Answer

No, because the Law of Sines gives sin F = 1

Question 3

Using the Law of Sines, if angle A = 120° and angle B = 40°, what is angle C?

Accepted Answer

20°

Answer

80°

Answer

100°

Answer

140°

Question 4

Two forces of 50 N and 70 N act on an object at an angle of 130° between them. What is the magnitude of the resultant force?

Accepted Answer

√(2500 + 4900 + 7000·cos 130°)

Answer

√(2500 + 4900 − 7000·cos 50°)

Answer

√(2500 + 4900 − 7000·cos 130°)

Answer

√(50² − 70²)

Question 5

Which condition guarantees the ambiguous SSA case produces exactly TWO distinct triangles?

Accepted Answer

b·sin A < a < b (with A acute)

Answer

a > b

Answer

a = b·sin A

Answer

a < b·sin A

Question 6

In triangle RST, R = 65°, r = 18, s = 15. Applying the Law of Sines, what is sin S?

Accepted Answer

sin S = 15·sin 65° / 18

Answer

sin S = 18·sin 65° / 15

Answer

sin S = sin 65° / (15·18)

Answer

sin S = 15 / (18·sin 65°)

Question 7

A pilot flies 200 miles north, then turns and flies 150 miles on a bearing of N 60° E. How far is the pilot from the starting point?

Accepted Answer

√(40000 + 22500 − 60000·cos 60°)

Answer

√(40000 + 22500 + 60000·cos 60°)

Answer

√(40000 + 22500 − 60000·cos 120°)

Answer

√(40000 − 22500)