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 \\(\frac{kl}{jl}\\). choose 1 answer: a 0.64, b 0.77, c 0.83, d 1.2

Explanation:

Step1: Identify angle and sides

In right triangle $JKL$, $\angle J = 40^\circ$, $\angle L = 90^\circ$. $\frac{KL}{JL}$ is $\tan(40^\circ)$, since $KL$ is opposite $\angle J$, $JL$ is adjacent to $\angle J$, and $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Match to given triangle

Use triangle 3: it has a $40^\circ$ angle, opposite side $6.4$, adjacent side $7.7$.

Step3: Calculate the ratio

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

Answer:

C. 0.83