Question

1. find the value of the trigonometry ratio below. give the answer in both fraction and decimal form. (see yellow hint below.) what is tan z? (fraction form) (decimal form)

Explanation:

Step1: Recall the tangent ratio formula

$\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$
For angle $Z$, the opposite side is $XY = 9$ and the adjacent side is $YZ=12$.

Step2: Calculate the tangent ratio in fraction form

$\tan Z=\frac{9}{12}=\frac{3}{4}$ (simplify the fraction by dividing numerator and denominator by 3)

Step3: Calculate the tangent ratio in decimal form

$\frac{3}{4}=3\div4 = 0.75$

Answer:

Fraction form: $\frac{3}{4}$; Decimal form: $0.75$