Question

In ΔJKL, the measure of ∠L=90°, JL = 24, LK = 7, and KJ = 25. What is the value of the sine of ∠K to the nearest hundredth?

Answer 1

Given:

Given that JKL is a right triangle.

The measure of ∠L is 90°

The length of JL = 24, LK = 7, and KJ = 25.

We need to determine the value of sine of ∠K.

Value of sin ∠K:

The value of sin ∠K can be determine using the trigonometric ratio.

Thus, we have;

$sin \ \theta=\frac{opp}{hyp}$

Substituting $\theta=K$, the side opposite to angle K is JL and the hypotenuse is JK

Thus, we have;

$sin \ K=\frac{JL}{JK}$

Substituting JL = 24 and JK = 25, we get;

$sin \ K=\frac{24}{25}$

Simplifying, we get;

$sin \ K=0.96$

     $K=sin^{-1}(0.96)$

     $K=73.74^{\circ}$

Thus, the measure of sine of ∠K is 73.74°