In right triangle JKL, ∠L is a right angle, m∠J=62∘, and JK=17.
sin62∘≈0.88
cos62∘≈0.47
tan62∘≈1.88
Triangle J K L as described in the text.
What is the measurement of JL?
If necessary, round your answer to one decimal place, like this: 42.5
To find the measurement of JL, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, JL is the hypotenuse of right triangle JKL.
Given that JK = 17, we need to find the measurement of JL.
Using the Pythagorean theorem, we have:
JL^2 = JK^2 + KL^2
Substituting the known values, we get:
JL^2 = 17^2 + KL^2
Since ∠J = 62∘, we can use trigonometric ratios to find KL.
We are given:
sin62∘ ≈ 0.88
cos62∘ ≈ 0.47
tan62∘ ≈ 1.88
To find KL, we can use the sine ratio:
sinθ = opposite/hypotenuse
In this case, θ = ∠J and the opposite side is KL, while the hypotenuse is JL.
So we have:
sin62∘ = KL/JL
Rearranging the equation, we can solve for KL:
KL = JL * sin62∘
Now we can substitute this into our original equation:
JL^2 = 17^2 + (JL * sin62∘)^2
Simplifying further:
JL^2 = 289 + JL^2 * sin^2(62∘)
Moving all terms to one side:
0 = 289 + JL^2 * sin^2(62∘) - JL^2
Simplifying the equation:
0 = 289 + JL^2 * (sin^2(62∘) - 1)
Rearranging:
JL^2 * (sin^2(62∘) - 1) = -289
Dividing both sides by (sin^2(62∘) - 1):
JL^2 = -289/(sin^2(62∘) - 1)
Rounding the value of JL to one decimal place:
JL ≈ 19.5
Therefore, the measurement of JL is approximately 19.5.