Question

Right triangles 1, 2, and 3 are given with all their angle measures and approximate side lengths. Use one of the triangles to approximate the ratio (KL)/(JL).

- 0.64
- 0.77
- 0.83
- 1.2

Answer 1

Answer: it’s 0.82

Explanation:

Answer 2

`(KL)/(JL)` =
`(6.4)/(7.7)` = 0.83

Explanation:

The key understanding here is that ΔJKL is similar to triangle 3 based on the AA criterion (they both have a right angle and a 40° angle).

We can find
`(KL)/(JL)` by setting up a proportion statement that includes KL, JL, and the lengths of their corresponding sides in triangle 3.

We can use this proportion:

`(KL)/(6.4)` =
`(JL)/(7.7)`

`(KL)/(6.4)` ⇒ opposite to 40° angle

KL, JL ⇒ ΔJKL

`(JL)/(7.7)` ⇒ adjacent to 40° angle

6.4, 7.7 ⇒ triangle 3

[Now see the attachment]

Now we can rewrite the equation to show the ratios of the side lengths within each triangle.

`(KL)/(JL)` =
`(6.4)/(7.7)`

`(KL)/(JL)` ⇒ ΔJKL

KL, 6.4 ⇒ adjacent to 40° angle

`(6.4)/(7.7)` ⇒ triangle 3

JL, 7.7 ⇒ adjacent to 40° angle