Question

In triangle △JKL, ∠JKL is right angle, and KM is an altitude. JK=24 and JM=18, find JL.

Answer 1

The length of JL is approximately 15.87 units.

To find the length of JL, we can use the Pythagorean theorem.

In triangle △JKL, ∠JKL is a right angle, and KM is an altitude.

Since JK=24 and JM=18, we can use these lengths to find JL.

Let's label the length of JL as x.

Using the Pythagorean theorem, we have:

`JL^2 = JK^2 - JM^2`

`x^2 = 24^2 - 18^2`

`x^2 = 576 - 324`

`x^2 = 252`

x = √252

Therefore, the length of JL is approximately 15.87 units.

Answer 2

JL ≈ 32

Explanation:

The triangle JKL has a side of JK = 24 and we are asked to find side JL. The triangle JKL is a right angle triangle.

Let us find side the angle J first from the triangle JKM. Angle JMN is 90°(angle on a straight line).

using the cosine ratio

cos J = adjacent/hypotenuse

cos J = 18/24

cos J = 0.75

J = cos⁻¹ 0.75

J = 41.4096221093

J ≈ 41.41°

Let us find the third angle L of the triangle JKL .Sum of angle in a triangle = 180°. Therefore, 180 - 41.41 - 90 = 48.59

Angle L = 48.59 °.

Using sine ratio

sin 48.59 ° = opposite/hypotenuse

sin 48.59 ° = 24/JL

cross multiply

JL sin 48.59 ° = 24

divide both sides by sin 48.59 °

JL = 24/sin 48.59 °

JL = 24/0.74999563751

JL = 32.0001861339

JL ≈ 32