Question

In △XYZ, x=410 inches, y=450 inches, and z=210 inches. Find the measure of ∠X to the nearest degree.

a) 29°
b) 37°
c) 46°
d) 53°

Answer 1

To find the measure of angle X in triangle XYZ, you can use the Law of Cosines.

Step-by-step explanation:

To find the measure of angle X in triangle XYZ, we can use the Law of Cosines. This law states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides, minus twice their product, multiplied by the cosine of the angle between them. In this case, we have the following equation:

x^2 = y^2 + z^2 - 2yz * cos(X)

Substituting the given values, we get:

(410)^2 = (450)^2 + (210)^2 - 2(450)(210) * cos(X)

Solving for cos(X), we find cos(X) = -0.484. Taking the inverse cosine of -0.484 gives us the measure of angle X to the nearest degree, which is approximately 129°.