Question

Find AB.
Round to the nearest tenth.
61°

Answer 1

AB~ 14.3 i believe but Im not sure

Answer 2

AB ≈ 14.3

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:

`c^2=a^2+b^2-2abcos(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

`c=AB\\a=BC=16\\b=CA=5\\C=m\angle C=61^(\circ)`

Substituting these values into the law of cosines:

`c^2=16^2+5^2-2(16)(5)\cos{61^(\circ)}\\c^2=256+25-160\cos{61^(\circ)}\\c^2=281-160\cos{61^(\circ)}\\c=\sqrt{281-160\cos{61^(\circ)}}\\c\approx 14.3`