the angle of elevation from l to k measure 24. if kl=19 find jl and round to the nearest tenth
We have a rt. triangle; the hyp is kl
and the hor side is jl. The angle between the hor side and hyp = 24 deg.
jl = 19cos24 = 17.4.
jk = 19sin24 = 7.7.
correct henry it is 17.4
To find the length of JL, we will use the tangent of the angle of elevation.
Tangent (θ) = Opposite side / Adjacent side
In this case, the opposite side is JK, and the adjacent side is KL.
Tangent (θ) = JK / KL
We know that KL (the adjacent side) is 19 and the angle of elevation is given as 24 degrees. Therefore,
Tangent (24 degrees) = JK / 19
Now, we can solve for JK (the opposite side) by rearranging the equation:
JK = Tan (24 degrees) * 19
Using a calculator, we can find the tangent of 24 degrees, which is approximately 0.4450.
JK ≈ 0.4450 * 19
JK ≈ 8.455
Therefore, the length of JL rounded to the nearest tenth is approximately 8.5.
To find the length of JL, we first need to determine the trigonometric relationship between the sides of triangle LJK using the given angle of elevation.
In this case, we have the opposite side (JK) and the hypotenuse (KL). To find the adjacent side (JL), we can use the trigonometric function tangent (tan).
The tangent of an angle is equal to the ratio of the opposite side to the adjacent side.
tan(angle) = opposite / adjacent
tan(24) = JK / JL
Now we can solve for JL:
JL = JK / tan(24)
Given that KL = 19 and the tangent of 24 degrees is approximately 0.445, we can substitute these values into our equation:
JL = 19 / 0.445 ≈ 42.6949153
Rounding to the nearest tenth, JL is approximately 42.7.