Question

In triangle XYZ, side X=16cm side Y=14cm and side Z=15cm . Calculate the size of angle X to the nearest degrees and minute?

Answer 1

To find the size of angle X, we can use the Law of Cosines.

The Law of Cosines states that in any triangle with sides a, b, and c, and angle A opposite side a:

a^2 = b^2 + c^2 - 2bc * cos(A)

Plugging in the values given, we can calculate angle X:

16^2 = 14^2 + 15^2 - 2(14)(15) * cos(X)

Simplifying further:

256 = 196 + 225 - 420 * cos(X)
256 = 421 - 420 * cos(X)

Rearranging the equation:

420 * cos(X) = 421 - 256
420 * cos(X) = 165
cos(X) = 165/420
cos(X) = 0.39285714

Now, we can use the inverse cosine function to find the angle X:

X = cos^(-1)(0.39285714)
X ≈ 67.768 degrees

To get the answer in minutes, we can multiply the decimal part of the angle (0.768) by 60:

Minutes = 0.768 * 60
Minutes ≈ 46

Therefore, the size of angle X is approximately 67 degrees and 46 minutes.