The angle of elevation from L to K measures 24°. If KL = 19, find JL. Round your answer to the nearest tenth.
KL/JL = tan 24°
you know KL, so now just solve for JL.
To find JL, we need to use trigonometry. In this case, we can use the tangent function.
Tangent is defined as the ratio of the length of the opposite side to the length of the adjacent side of a right triangle. In our case, the angle of elevation is given, so the side opposite to the angle of elevation is JL and the side adjacent to the angle of elevation is KL.
The formula for tangent is: tan(angle) = opposite/adjacent.
Let's plug in the values we have:
tan(24°) = JL/19.
To isolate JL, we can multiply both sides of the equation by 19:
19 * tan(24°) = JL.
Using a calculator, we can find that tan(24°) is approximately 0.44504187.
Now we can substitute this value into the equation:
19 * 0.44504187 = JL.
JL ≈ 8.45579193.
Rounding to the nearest tenth, JL is approximately 8.5.