Answer:
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:
[tex]c^2=a^2+b^2-2ab\cos{C}[/tex]
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
[tex]c=AB\\a=BC=16\\b=CA=5\\C=m\angle C=61^{\circ}[/tex]
Substituting these values into the law of cosines:
[tex]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[/tex]
