Question 1

Given triangle ABC with $$A = 40^\circ$$, $$B = 60^\circ$$, and $$a = 4$$, which equation correctly sets up the Law of Sines to solve for side $$b ($$opposite angle $$B$$)?

Accepted Answer

$$\displaystyle \frac{b}{\sin 60^\circ} = \frac{4}{\sin 40^\circ}$$

Question 2

A surveyor is measuring a triangular plot of land. She knows two angles, $$35^\circ$$ and $$15^\circ$$, and the side between them is $$5$$ meters. What is the measure of the third angle?

Accepted Answer

$$130^\circ$$

Question 3

Given triangle ABC with $$a = 3$$, $$b = 2$$, and $$A = 40^\circ$$, which equation would you use to solve for angle $$B$$ using the Law of Sines?

Accepted Answer

$$\displaystyle \frac{2}{\sin B} = \frac{3}{\sin 40^\circ}$$

Question 4

A triangle has sides $$a = 1$$, $$b = 2$$, and angle $$C = 50^\circ. $$When you attempt to solve for angle $$A$$ using the Law of Sines, you find $$\sin A = 1.0531. $$What does this indicate about the triangle?

Accepted Answer

There is no solution; the triangle cannot exist.

Question 5

In the ambiguous SSA case, triangle ABC has $$a = 1$$, $$b = 2$$, and $$C = 25^\circ. $$Solving for angle $$A$$ gives $$\sin A = 0.8452. $$What are the possible values for angle $$A$$?

Accepted Answer

$$57.7^\circ$$ and $$122.3^\circ$$

Question 6

A triangle has $$A = 40^\circ$$, $$a = 4$$, and $$c = 3. $$Using the Law of Sines, you find $$\sin C = 0.4821. $$What is the value of angle $$C$$?

Accepted Answer

$$82.28^\circ$$

Question 7

A triangle has $$A = 40^\circ$$, $$a = 4$$, and $$c = 5. $$Solving for angle $$C$$ gives $$\sin C = 0.8035. $$What are the possible values for angle $$C$$?

Accepted Answer

$$46.53^\circ$$ and $$126.54^\circ$$

Question 8

A triangle has $$A = 15^\circ$$, $$B = 35^\circ$$, and $$c = 5. $$What is the length of side $$a ($$opposite angle $$A$$)?

Accepted Answer

$$a \approx 1.69$$

Question 9

A triangle has $$A = 40^\circ$$, $$a = 4$$, and $$c = 3. $$After finding $$C = 82.28^\circ$$, what is the measure of angle $$B$$?

Accepted Answer

$$111.18^\circ$$

Question 10

A triangle has $$A = 40^\circ$$, $$a = 4$$, and $$c = 5. $$After finding $$C = 46.53^\circ$$, what is the measure of angle $$B$$?

Accepted Answer

$$93.47^\circ$$

Question 11

A triangle has $$A = 40^\circ$$, $$a = 4$$, and $$c = 5. $$After finding $$C = 126.54^\circ$$, what is the measure of angle $$B$$?

Accepted Answer

$$13.46^\circ$$

Question 12

A triangle has $$A = 40^\circ$$, $$a = 4$$, and $$c = 5. $$For the solution where $$C = 46.53^\circ$$, what is the length of side $$b ($$opposite angle $$B$$)?

Accepted Answer

$$b \approx 6.12$$

Question 13

A triangle has $$A = 40^\circ$$, $$a = 4$$, and $$c = 5. $$For the solution where $$C = 126.54^\circ$$, what is the length of side $$b ($$opposite angle $$B$$)?

Accepted Answer

$$b \approx 1.45$$

Question 14

Which of the following is NOT a valid case for using the Law of Sines to solve a triangle?

Accepted Answer

SSS (Side-Side-Side)

Question 15

A triangle has $$a = 3$$, $$b = 2$$, and $$A = 40^\circ. $$After solving for $$B$$, you find $$B = 37.25^\circ. $$What is the measure of angle $$C$$?

Accepted Answer

$$102.75^\circ$$

Question 16

A triangle has $$A = 15^\circ$$, $$B = 35^\circ$$, and $$c = 5. $$What is the length of side $$b ($$opposite angle $$B$$)?

Accepted Answer

$$b \approx 2.74$$

Question 17

A triangle has $$A = 40^\circ$$, $$a = 4$$, and $$c = 3. $$After finding $$C = 82.28^\circ$$ and $$B = 57.72^\circ$$, what is the length of side $$b ($$opposite angle $$B$$)?

Accepted Answer

$$b \approx 5.39$$

Question 18

A triangle has $$A = 25^\circ$$, $$a = 1$$, and $$b = 2. $$After finding two possible values for angle $$A$$, what is the sum of the two possible values for angle $$B$$?

Accepted Answer

$$97.3^\circ + 32.7^\circ = 130^\circ$$

The Law of Sines: Solving Non-Right Triangles 6.1

Study Guide - Practice Questions

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