Question

Triangle J K L is shown. Angle K L J is a right angle. The length of hypotenuse K J is 10.9 centimeters and the length of L J is 8.9 centimeters. Angle L K J is x.
Which equation can be used to find the measure of angle LKJ?

cos−1(StartFraction 8.9 Over 10.9 EndFraction) = x
cos−1(StartFraction 10.9 Over 8.9 EndFraction) = x
sin−1(StartFraction 10.9 Over 8.9 EndFraction) = x
sin−1(StartFraction 8.9 Over 10.9 EndFraction) = x

Answer 1

sin^{-1}(8.9/10.9) = x

Reason: angle at K has opposite side LJ = 8.9 and hypotenuse KJ = 10.9, so sin x = opposite/hypotenuse = 8.9/10.9, hence x = arcsin(8.9/10.9).