Find AB.
Round to the nearest tenth.
61°

AB ≈ 14.3

Step-by-step explanation:

We're given two sides (BC and CA) and an angle (C) between them; the law of cosines is a good tool for calculating the third side of the triangle here. To remind you, the law of cosines tells us the relationship between the sides of a triangle with side lengths a, b, and c:

Where C is the angle between sides a and b. c is typically the side we're trying to find, so on our triangle, we have

Substituting these values into the law of cosines:

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation: