Question

on which triangle can the law of cosines be applied once to find an unknown angle measure? law of cosines: a² = b² + c² - 2bc cos(a)

Explanation:

Step1: Recall law - of - cosines condition

The law of cosines $a^{2}=b^{2}+c^{2}-2bc\cos(A)$ can be used to find an unknown angle when we know the lengths of all three sides of a triangle.

Step2: Analyze each option

In the first right - triangle, we have a right - angle and two side - lengths. We can use trigonometric ratios for right - triangles instead of the law of cosines. In the second triangle, we only know the length of one side, so we can't use the law of cosines. In the third triangle, if we know the lengths of all three sides (assuming we know the length of side $y$), we can use the law of cosines to find an unknown angle.

Answer:

The third triangle (where we know the lengths of all three sides)