Find the sine of ∠K.
36
77
85
K
J
I
Simplify your answer and write it as a proper fraction, improper fraction, or whole number.
Check what you typed, how it came out, and if it makes sense to you.
To find the sine of ∠K, we need to know the lengths of the sides of the triangle where ∠K is located. From the given information, we have 36, 77, and 85, but we don't know how these sides are related to ∠K.
To determine which side length is opposite ∠K, we should label the triangle. Let's call the vertex opposite ∠K as point J and the remaining two vertices as point I and point S.
Now, based on the given information, we know that side JK has a length of 36, side IJ has a length of 77, and side IS has a length of 85.
Next, we need to identify which side is opposite ∠K. By convention, the side opposite an angle is usually labeled with the same letter as the vertex of the angle. Therefore, in this case, side JK is opposite ∠K.
Now that we have identified the side opposite ∠K, we can calculate the sine of ∠K. The sine of an angle in a right triangle is defined as the length of the side opposite the angle divided by the length of the hypotenuse.
In our case, the side opposite ∠K is JK with a length of 36, and the hypotenuse is IS with a length of 85.
So the sine of ∠K is 36/85.
To simplify this answer, we need to check if the numerator and denominator have any common factors. In this case, 36 and 85 do not have any common factors, so the fraction 36/85 is already in its simplest form. Therefore, the sine of ∠K is 36/85.