You can use the law of sinesto solvethis problem.Becauseyou haveone side and the angleopposite,you
can find the constantthat appliesto the entiretriangle.This ratio will be equalto the proportionof side
and angle. You can use your calculatorto find the valueof the sines.
So, usingthe law of sines,the anglelabeled mustmeasureabout.
The Law of Cosines
Thereis anotherlaw that workson acuteand obtusetrianglesin additionto right triangles.TheLaw of
Cosinesuses the cosineratio to identifyeitherlengthsof sidesor missingangles.To use the law of cosines,
you musthaveeitherthe measuresof all threesides,or the measureof two sidesand the measureof the
includedangle.
It doesn’tmatterhow you assignthe variablesto the threesidesof the triangle,but the angle mustbe
oppositeside.
Example 3
Examinethe trianglein the followingdiagram.