This involves Trigonometric Equations, Law of Cosines, Law of Sines, Triangle Applications.1. Solve the triangle:

possible, say so.

. If it is not

This triangle is not solvable.

2. Find the side length, x, of the given triangle.

3.

Solve the given equation over the interval

4.

Use Heron’s Formula, that is, the area of a triangle is

triangle contains sides a, b and c and

lengths:

, where the

to find the area of the triangle with side

.

0.65 square units

2.33 square units

1.5 square units

3.9 square units

5. Solve the given equation over the interval [0, 2π): csc2 x + 2 csc x = 0.

x = 0 and x = 2π

6.

Solve the triangle:

. If it is not possible, say so.

This triangle is not solvable.

7. If possible, find the area of the triangle defined by the following: a = 1.2, c = 2.1, β = 5°.

1.26 square units

2.2 square units

1.89 square units

0.11 square units

8. Solve the given equation over the interval [0, 2π): sec2 x = 1.

x = 0 and x = 2π

x = 0 and x = π

9. If possible, find the area of the triangle defined by the following: b = 11, c = 8, a = 28°.

44 square units

21.8 square units

74.8 square units

20.7 square units

10. Solve the given equation over the interval [0, 2π): 2 cos x − sin2 x = cos2 x.

11.

Solve the triangle:

. If it is not possible, say so.

This triangle is not solvable.

12.

Solve the triangle:

. If it is not possible, say so.

This triangle is not solvable.

13. Solve the triangle: a = 20, b = 10, c = 15. If it is not possible, say so.

This triangle is not solvable.

14. Solve the triangle: a = 7, b = 9, C = 100°. If it is not possible, say so.

This triangle is not solvable.

15.

Use Heron’s Formula, that is, the area of a triangle is

triangle contains sides a, b and c and

lengths: a = 12.4, b = 13.7, c = 20.2.

, where the

to find the area of the triangle with side

138.4 square units

125.2 square units

84.9 square units

83.3 square units

16. Solve the given equation over the interval [0, 2π): 6 sin2 x − 5 sin x + 1 = 0.

17.

Use Heron’s Formula, that is, the area of a triangle is

, where the

triangle contains sides a, b and c and

lengths:

to find the area of the triangle with side

.

0.06 square units

0.1 square units

0.04 square units

0.08 square units

18. Find the measurement of angle A.

19. Solve the triangle: a = 10, b = 10, c = 15. If it is not possible, say so.

This triangle is not solvable.

20. The triangle described is of the form SSA. Determine if there is no triangle possible, one triangle

possible, or two triangles possible. If only one triangle is possible, solve the triangle. If either two

triangles may be formed or no triangle may be formed, say so. The triangle is defined

by:

Two triangles may be formed.

No triangle can be formed from this information.

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