We have been given that in ΔIJK, the measure of ∠K=90°, KJ = 77, IK = 36, and JI = 85. We are asked to find the ratio that represents the cosine of angle I.
First of all, we will draw a right triangle as shown in the attachment.
We know that cosine relates adjacent side of right triangle with hypotenuse.
[tex]\text{cos}=\frac{\text{Adjacent}}{\text{Hypotenuse}}[/tex]
We can see that adjacent side to angle I is IK and hypotenuse is IJ.
[tex]\text{cos}(\angle I)=\frac{IK}{IJ}[/tex]
[tex]\text{cos}(\angle I)=\frac{36}{85}[/tex]
Therefore, the ratio of cosine of angle I is [tex]\frac{36}{85}[/tex].
