Question

trigonometric ratios

1. find the exact value of tan j in simplest radical form

(image of a right triangle with right angle at i, sides: ih=20, ij=15, hj=25)

Explanation:

Step1: Recall tan definition

In a right triangle, $\tan\theta = \frac{\text{opposite}}{\text{adjacent}}$ to $\theta$.
For $\angle J$, opposite side is $IH = 20$, adjacent side is $IJ = 15$.

Step2: Calculate tan J

$\tan J = \frac{IH}{IJ} = \frac{20}{15}$

Step3: Simplify the fraction

Simplify $\frac{20}{15}$ by dividing numerator and denominator by 5: $\frac{20\div5}{15\div5} = \frac{4}{3}$.

Answer:

$\frac{4}{3}$