Question

In ΔJKL, the measure of ∠L=90°, KL = 22 feet, and JK = 54 feet. Find the measure of ∠J to the nearest degree.

Answer 1

We have been given that in ΔJKL, the measure of ∠L=90°, KL = 22 feet, and JK = 54 feet. We are asked to find the measure of angle J to nearest degree.

First of all, we will draw a triangle as shown in the attachment.

We can see from our attachment that side KL is opposite side to angle J and side JK is hypotenuse of right triangle.

We know that sine relates opposite side of right triangle to hypotenuse.

$\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}$

$\text{sin}(\angle J)=\frac{22}{54}$

Using inverse sine or arcsin, we will get:

$\angle J=\text{sin}^{-1}(\frac{22}{54})$

$\angle J=24.042075905756^{\circ}$

Upon rounding to nearest degree, we will get:

$\angle J\approx 24^{\circ}$

Therefore, the measure of angle J is approximately 24 degrees.