Question

Find the sine, cosine, and tangent of ∠K.

image of a right triangle that has the following values, Angle J, Angle K, Angle I, Line JK which has a length of 97, Line KI which has an unknown length, and Line JI which has a length of 72

Answer 1

Assume JK = 97 is the hypotenuse (largest side) and JI = 72 is the side opposite ∠K. Then the other leg KI = sqrt(97^2 − 72^2) = sqrt(9409 − 5184) = sqrt(4225) = 65.

Thus
- sin K = opposite/hypotenuse = 72/97
- cos K = adjacent/hypotenuse = 65/97
- tan K = opposite/adjacent = 72/65

(Decimals: sin K ≈ 0.7423, cos K ≈ 0.6701, tan K ≈ 1.1077.)