Question

In △ XYZ, z=6.8 inches, m∠ Z=26° and m∠ X=132°. Find the length of y, to the nearest 10th of an inch.

Answer 1

To find the length of y in triangle XYZ, use the Law of Sines. Solve for y using the given values of z, X, and Z. Round the result to the nearest 10th of an inch.

Step-by-step explanation:

To find the length of y in triangle XYZ, we can use the Law of Sines. The Law of Sines states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant. In this case, we have:

(y / sin(X)) = (z / sin(Z))

Substituting the given values, we have:

(y / sin(132°)) = (6.8 / sin(26°))

Using a calculator to compute the sines of the angles, we find that sin(132°) ≈ -0.727 and sin(26°) ≈ 0.438. Solving for y, we get:

y ≈ (6.8 * sin(132°)) / sin(26°) ≈ -9.145

Since length can't be negative, the length of y to the nearest 10th of an inch is approximately 9.1 inches.

Answer 2

To find the length of side y in triangle XYZ, we used the Law of Sines with the given side z and angles Z and X, and the sum of angles in a triangle. After computing, we found that y is approximately 5.8 inches when rounded to the nearest tenth.

Step-by-step explanation:

The problem is to find the length of side y in triangle XYZ, given side z and the measures of angles Z and X. To solve this, we use the Law of Sines, which states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides and angles of a triangle.

First, we find the measure of angle Y using the fact that the sum of angles in a triangle is 180 degrees: m∠Y = 180° - 26° - 132° = 22°.

Then, we set up the Law of Sines ratio as:

• z / sin(Z) = y / sin(Y)
• 6.8 inches / sin(26°) = y / sin(22°)

Next, we solve for y:

• y = sin(22°) * (6.8 inches / sin(26°))
• y ≈ sin(22°) * (6.8 / 0.4384)
• y ≈ 0.3746 * 15.504
• y ≈ 5.805 inches

Round y to the nearest tenth of an inch:

y ≈ 5.8 inches