Question

In ΔIJK the measure of ∠K=90, IK =21, KJ =20 and JI=29. What is the value of the cosine of ∠J to the nearest hundredth

Answer 1

Since the measure of ∠K is 90º, we're dealing with a right triangle, where JI is the hypotenuse and KJ and IK the legs.

In a right triangle, the cosine of an angle is given by the ratio between the adjacent leg and the hypotenuse. The adjacent leg to ∠J is KJ and its measure is 20, the hypotenuse is JI and its measure is 29, therefore, their ratio is

`\cos (J)=(20)/(29)=0.68965517241\ldots\approx0.69`

And this is our answer.