Question

1. if the tangent ratio of $\theta$ is $\frac{12}{5}$, which angle is $\theta$?

(image of a right triangle with right angle at l, legs: jl = 5 in, lk = 12 in, hypotenuse jk = 13 in, vertices j, l, k)

Explanation:

Step1: Recall Tangent Ratio Definition

Tangent of an angle in a right triangle is $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Analyze Angles in Triangle

• For $\angle J$: Opposite side to $\angle J$ is $LK = 12$ in, adjacent side is $JL = 5$ in. So $\tan(J)=\frac{12}{5}$.
• For $\angle K$: Opposite side to $\angle K$ is $JL = 5$ in, adjacent side is $LK = 12$ in. So $\tan(K)=\frac{5}{12}$.

Given $\tan(\theta)=\frac{12}{5}$, so $\theta$ is $\angle J$.

Answer:

$\theta$ is $\angle J$ (or angle at vertex J)