Question 1

Given triangle $$ABC$$ with $$a = 5$$, $$b = 7$$, and $$C = 45^\circ$$, which version of the Law of Cosines should you use to find side $$c$$?

Accepted Answer

$$c^2$$ = $$a^2$$ + $$b^2 - 2ab$$ \cos C$$

Question 2

A triangle has sides $$a = 8$$, $$b = 6$$, and $$c = 10. $$What is the measure of angle $$A to $$the nearest degree?

Accepted Answer

$$A \approx 36^\circ$$

Question 3

Which of the following scenarios is most appropriate for using the Law of Cosines?

Accepted Answer

Given all three sides (SSS)

Question 4

A surveyor measures two sides of a triangular plot as $$a = 120 m$$, $$b = 150 m$$, and the included angle $$C = 100^\circ. $$What is the length of the third side $$c$$? (Round to the nearest meter)

Accepted Answer

$$c \approx 238 m$$

Question 5

Given triangle $$ABC$$ with $$a = 4$$, $$b = 4$$, and $$c = 6$$, what type of triangle is this and what is the measure of angle $$C$$?

Accepted Answer

Isosceles, $$C \approx 117.28^\circ$$

Question 6

A pilot flies 200 miles north, then turns $$40^\circ$$ east of north and flies another 120 miles. How far is the pilot from the starting point? (Round to the nearest mile)

Accepted Answer

$$\approx 306$$ miles

Question 7

If $$a = 5$$, $$b = 7$$, and $$c = 8$$, what is $$\cos A$$ using the Law of Cosines?

Accepted Answer

$$\cos A = \dfrac{5^2$ + 7^2$ - 8^2$}{2 \cdot 5 \cdot 7}$$

Question 8

A triangle has sides $$a = 9$$, $$b = 12$$, and $$c = 15. $$What is the measure of angle $$B to $$the nearest degree?

Accepted Answer

$$B \approx 73^\circ$$

Question 9

Which of the following is NOT a valid form of the Law of Cosines?

Accepted Answer

$$a^2$$ = $$b^2$$ + $$c^2 - 2ab$$ \cos C$$

Question 10

A triangle has sides $$a = 7$$, $$b = 8$$, and $$c = 9. $$Which method is best to find angle $$B$$?

Accepted Answer

Law of Cosines

Question 11

A triangle has $$a = 10$$, $$b = 12$$, and $$C = 60^\circ. $$What is the value of $$c$$? (Round to the nearest tenth)

Accepted Answer

$$c \approx 13.2$$

Question 12

A triangle has sides $$a = 5$$, $$b = 5$$, and $$c = 8. $$What is the measure of angle $$C to $$the nearest degree?

Accepted Answer

$$C \approx 104^\circ$$

Question 13

A triangle has $$a = 3$$, $$b = 3$$, and $$c = 2. $$What is the measure of angle $$A$$?

Accepted Answer

$$A \approx 70.53^\circ$$

Question 14

A triangle has $$a = 6$$, $$b = 8$$, and $$C = 120^\circ. $$What is the length of side $$c$$? (Round to the nearest tenth)

Accepted Answer

$$c \approx 13.9$$

Question 15

A triangle has sides $$a = 10$$, $$b = 15$$, and $$c = 20. $$What is the largest angle in the triangle?

Accepted Answer

$$C$$

Question 16

A triangle has $$a = 7$$, $$b = 9$$, and $$C = 110^\circ. $$What is the value of $$c$$? (Round to the nearest tenth)

Accepted Answer

$$c \approx 13.2$$

Question 17

A triangle has sides $$a = 6$$, $$b = 8$$, and $$c = 10. $$What is the measure of angle $$C to $$the nearest degree?

Accepted Answer

$$C \approx 90^\circ$$

Question 18

A triangle has $$a = 5$$, $$b = 12$$, and $$c = 13. $$What is the measure of angle $$A to $$the nearest degree?

Accepted Answer

$$A \approx 22^\circ$$

Question 19

A triangle has $$a = 10$$, $$b = 10$$, and $$C = 120^\circ. $$What is the value of $$c$$? (Round to the nearest tenth)

Accepted Answer

$$c \approx 17.3$$

The Law of Cosines: Solving Non-Right Triangles 6.2

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