1.
Solve the triangle.
A = 46°, a = 31, b = 27 (5 points)
B = 38.8°, C = 115.2°, c 34.3
B = 38.8°, C = 95.2°, c 25.7
B = 38.8°, C = 95.2°, c 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 5.8
No triangle is formed.
C = 21.8°, A = 21.2°, a 5.8
5.
Solve the triangle.
A = 52°, b = 10, c = 7 (5 points)
a 12, C 47.9, B 80.1
a 7.9, C 43.9, B 84.1
No triangles possible
a 12, C 43.9, B 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
