Question

In Δxyz, x = 42 inches, y = 88 inches and ∠z=90°. find ∠x, to the nearest degree.

Answer 1

In triangle XYZ, with x = 42 inches, y = 88 inches, and ∠Z = 90°, we can use the Pythagorean theorem and the sine function to find ∠X. ∠X is approximately 25.3°.

Step-by-step explanation:

In triangle XYZ, the given measurements are: x = 42 inches, y = 88 inches, and ∠Z = 90°.

To find ∠X, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Using the Pythagorean theorem, we can calculate the length of side XZ:

XZ² = XY² + YZ²

XZ² = 42² + 88²

XZ² = 1764 + 7744

XZ² = 9508

XZ ≈ 97.5 inches

Now, we can use the sine function to find ∠X:

sin(∠X) = opposite/hypotenuse

sin(∠X) = XY/XZ

sin(∠X) = 42/97.5

∠X ≈ arcsin(42/97.5)

∠X ≈ 25.3° (to the nearest degree)