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:

$\frac{KL}{JL}$ = $\frac{6.4}{7.7}$ = 0.83

Step-by-step 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 $\frac{KL}{JL}$ 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:

$\frac{KL}{6.4}$ = $\frac{JL}{7.7}$

$\frac{KL}{6.4}$ ⇒ opposite to 40° angle

KL, JL ⇒ ΔJKL

$\frac{JL}{7.7}$ ⇒ 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.

$\frac{KL}{JL}$ = $\frac{6.4}{7.7}$

$\frac{KL}{JL}$ ⇒ ΔJKL

KL, 6.4 ⇒ adjacent to 40° angle

$\frac{6.4}{7.7}$ ⇒ triangle 3

JL, 7.7 ⇒ adjacent to 40° angle