1.
Solve the triangle.
A = 46°, a = 31, b = 27 (5 points)

B = 38.8°, C = 115.2°, c ‰ˆ 34.3

B = 38.8°, C = 95.2°, c ‰ˆ 25.7

B = 38.8°, C = 95.2°, c ‰ˆ 42.9

Cannot be solved
2.
State whether the given measurements determine zero, one, or two triangles.
A = 36°, a = 3, b = 9 (5 points)

Zero

Two

One
3.
Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles.
B = 40°, b = 25, c = 26 (5 points)

A = 98°, C = 42°, a = 16.2; A = 2°, C = 138°, a = 16.2

A = 98°, C = 42°, a = 38.5; A = 2°, C = 138°, a = 1.4

A = 92°, C = 48°, a = 38.9; A = 88°, C = 132°, a = 38.9

A = 92°, C = 48°, a = 16.1; A = 88°, C = 132°, a = 16.1
4.
Thegiven measurements may or may not determine a triangle. If not, thenstate that no triangle is formed. If a triangle is formed, then use theLaw of Sines to solve the triangle, if it is possible, or state that theLaw of Sines cannot be used.
B = 137°, c = 6, b = 11 (5 points)

The triangle cannot be solved with the Law of Sines.

C = 21.2°, A = 21.8°, a ‰ˆ 5.8

No triangle is formed.

C = 21.8°, A = 21.2°, a ‰ˆ 5.8
5.
Solve the triangle.
A = 52°, b = 10, c = 7 (5 points)

a ‰ˆ 12, C ‰ˆ 47.9, B ‰ˆ 80.1

a ‰ˆ 7.9, C ‰ˆ 43.9, B ‰ˆ 84.1

No triangles possible

a ‰ˆ 12, C ‰ˆ 43.9, B ‰ˆ 84.1
6.
Find the area of the triangle with the given measurements. Round the solution to the nearest hundredth if necessary.
A = 50°, b = 31 ft, c = 18 ft (5 points)

427.45 ft2

179.34 ft2

213.73 ft2

558 ft2
7.
Determinewhether a triangle can be formed with the given side lengths. If so,use Heron’s formula to find the area of the triangle. (5 points)
a = 240b = 121c = 302