The value of the sine of the angle J is equal to 5 / 13 (approx. 0.38).
The image attached aside shows us a right triangle with two known side lengths (JL, KJ) and a angle measure (m ∠ K).
The measure of the missing angle can be found by using the trigonometric function of cosine:
cos m ∠ J = KJ / JL
cos m ∠ J = 12 / 13
m ∠ J = 22.620°
The measure of the angle J within the triangle JKL is approximately 22.620°.
And the sine of the angle J, which helds the same positive sign than cosine as the angle is in the first quadrant on Cartesian plane, is:
sin m ∠J = √(1 - cos² m ∠J)
sin m ∠J = √[1 - (12 / 13)²]
sin m ∠J = 5 / 13
The value of the sine of the angle J is equal to 5 / 13 (approx. 0.38).
The probable question may be:
In triangle JKL, angle JKL=90 degree, JK=12, JL=13, Find the value of sin J rounded to the nearest hundredth.