The angle of elevation from L to K measures 39 degrees. If KL = 12, find JL. Round to nearest tenth.
My aluminum-foil clairvoyance cap is a bit foggy this morning, so I can't quite see your diagram.
I will assume you have a right-angled triangle KJL, where J is 90° and KL is the hypotenuse.
then cos 39° = JL/12
JL = 12cos39 = appr. 9.33
To find JL, we can use the trigonometric ratio of tangent.
Tangent of an angle is equal to the opposite side divided by the adjacent side.
In our case, the angle of elevation from L to K is 39 degrees and KL represents the opposite side, while JL represents the adjacent side.
Therefore, we can set up the equation as follows:
Tan(39 degrees) = KL / JL
Now, we can substitute the given values:
Tan(39 degrees) = 12 / JL
To find JL, we can rearrange the equation and solve for JL.
JL = 12 / tan(39 degrees)
Using a calculator, we can evaluate tan(39 degrees) and divide 12 by the result:
JL ≈ 12 / 0.80978403324386
JL ≈ 14.81 (rounded to the nearest tenth)
Therefore, JL is approximately 14.81 when rounded to the nearest tenth.
To find JL, we need to use trigonometry. In this case, we can use the tangent function. The tangent of an angle is equal to the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
Since the angle of elevation from L to K is 39 degrees, we can label this angle as ∠LJK. KL is given as 12 units.
Using the tangent function: tan(∠LJK) = opp/adj
tan(39°) = JL/KL
To isolate JL, we rearrange the equation:
JL = KL * tan(39°)
Substituting the given values:
JL = 12 * tan(39°)
Calculating this expression, we get:
JL ≈ 12 * 0.809
JL ≈ 9.712
Rounding to the nearest tenth, JL ≈ 9.7 units.
Therefore, JL is approximately 9.7 units.