Question

In ΔXYZ, x = 8.3 meters, y = 9 meters, and z = 15 meters. Find the remaining measurements of the triangle, and round your answers to the nearest tenth.
∠X = 56.9°, ∠Y = 66.6°, ∠Z = 56.5°
∠X = 28.6°, ∠Y = 31.2°, ∠Z = 120.2°
∠X = 56.9°, ∠Y = 66.6°, ∠Z = 120.2°
∠X = 28.6°, ∠Y = 31.2°, ∠Z = 56.5°

Answer 1

Answer:

The correct answer is B. ∠X = 28.6°, ∠Y = 31.2°, ∠Z = 120.2°

Step-by-step explanation:

Let's recall that for solving a SSS triangle, we :

1. Use the Law of Cosines first to calculate one of the angles

2. Use The Law of Cosines again to find another angle

3. Finally use angles of a triangle add to 180° to find the last angle.

1. Cos x = (9² + 15² - 8.3²/2 * 9 * 15)

Cos x = (81 + 225 - 68.89/270)

Cos x = 0.878

x = Cos ⁻¹ (0.878)

x = 28.6° (rounding to the next tenth)

2. Cos y = (8.3² + 15² - 9²/2 * 8.3 * 15)

Cos y = (68.89 + 225 - 81/249)

Cos y = 0.855

x = Cos ⁻¹ (0.855)

x = 31.2° (rounding to the next tenth)

3. z = 180 - 31.2 - 28.6

z = 120.2°

The correct answer is B. ∠X = 28.6°, ∠Y = 31.2°, ∠Z = 120.2°