Question

Triangle X Y Z is shown. The length of X Z is 12, the length of Y Z is 11, and the length of Y X is 6.

A scalene triangle has the lengths 6, 11, and 12. Keyla uses the law of cosines to find the measure of the largest angle. Complete her work and find the measure of angle Y to the nearest degree.

1. 122 = 112 + 62 − 2(11)(6)cos(Y)

2. 144 = 121 + 36 − (132)cos(Y)

3. 144 = 157 − (132)cos(Y)

4. −13 = −(132)cos(Y)

degrees

Answer 1

84 degrees

Explanation:

Applying the Cosine Rule (Choice 2 is the correct one) :-

12^2 = 11^2 + 6^2 - 2*11*6 cos Y

144 = 121 + 36 - 132 cos Y

cos Y = (121 + 36 - 144) / 132

cos Y = 0.09848

Y = 84.3 degrees