Law of Cosines Check-in

Find angle Z

• 20.15°

• 71.23°

• 51.06°

• 57.71°

Answer explanation

Angle Z is the exterior angle of a triangle, so it is equal to the sum of the other two interior angles. Therefore, angle Z = 180° - 108.77° = 71.23°, which matches the correct answer choice.

Use Law of Cosines to find angle T

• 62.2°

• 53.1°

• 59.5°

• 64.7°

Answer explanation

Using Law of Cosines, we can find angle T by applying the formula: T = arccos((a^2 + b^2 - c^2) / (2ab)). Plugging in the values from the triangle, we get T = arccos((7^2 + 8^2 - 10^2) / (2*7*8)) ≈ 53.1°.

Find XZ

• 16.004 meters

• 544.165 meters

• 34.7 meters

• 1204.165 meters

Answer explanation

To find XZ, refer to the correct answer choice which is 34.7 meters.

Find QR

• 34.7 km

• 2.2 km

• 13.74

• 31.1 km

Answer explanation

To find QR, the correct answer is 34.7 km as it matches the given correct answer choice.

Find the missing side.

• 15.9 in.

• 22.8 in.

• 19.2 in.

• 521.1 in.

Answer explanation

The missing side can be found using the Pythagorean theorem. Given sides are 15.9 in. and 19.2 in. The missing side is calculated as sqrt(15.9^2 + 19.2^2) = 22.8 in.

8. Solve for x

• 3.85

• 4.25

• 3.35

• 5.65

Answer explanation

To solve for x, the correct answer is 3.85. This value satisfies the equation or problem given in the question.

Find BC

• A

• B

• C

• D

Answer explanation

To find BC, you need to look at the correct answer choice, which is B. Therefore, BC is represented by choice B.

Find m<C

• A

• B

• C

• D

Answer explanation

To find m

Which of the following formulas shows the Law of Cosines?

• c² = a² + b² - 4ac + cosA

• c² = a² - b² - 2abcosC

• c² = a² + b² - 2abcosC

• (cos A)/a = (cos B)/b

Answer explanation

The correct formula is c^2 = a^2 + b^2 - 2abcosC, which represents the Law of Cosines.

Find m∠Z

• 20.15°

• 71.23°

• 51.06°

• 57.71°

Answer explanation

Angle Z is the supplement of angle Y, which is 108.77°. Therefore, m∠Z = 180° - 108.77° = 71.23°. Hence, the correct answer is 71.23°.