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

The remaining measurements of the triangle are ∠X = 56.9°, ∠Y = 66.6°, and ∠Z = 56.5°.

How to find measurements?

To find the remaining measurements of the triangle, use the Law of Cosines. The Law of Cosines states that in a triangle with sides x, y, and z, and opposite angles A, B, and C, the following equation holds:

z² = x² + y² - 2xy * cos(C)

Use this equation to find the missing side or angle in a triangle.

In this case, there are the following values:

x = 8.3 meters

y = 9 meters

z = 15 meters

To find the missing angles, ∠X, ∠Y, and ∠Z.

Using the Law of Cosines, write the following equations:

8.3² = x² + 15² - 2x × 15 ×cos(∠X)

9² = 15² + x² - 2x × 15 × cos(∠Y)

15² = x² + y² - 2xy × cos(∠Z)

Solve these equations for the missing angles using a calculator. The solutions are:

∠X = 56.9°

∠Y = 66.6°

∠Z = 56.5°

Therefore, the remaining measurements of the triangle are ∠X = 56.9°, ∠Y = 66.6°, and ∠Z = 56.5°.