Question

question 1
5 pts
find the value of the trigonometric ratio in reduced form.
find the value of the trigonometric ratio in reduced form.
\\(\tan z\\)
\\(\tan z =\\)

Explanation:

Step1: Recall tangent ratio formula

The tangent of an angle in a right - triangle is defined as $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. For $\angle Z$, the opposite side to $\angle Z$ is $XY = 21$ and the adjacent side to $\angle Z$ is $YZ=28$.
So, $\tan Z=\frac{XY}{YZ}$.

Step2: Substitute the side - lengths

Substitute $XY = 21$ and $YZ = 28$ into the formula: $\tan Z=\frac{21}{28}$.

Step3: Simplify the fraction

Find the greatest common divisor (GCD) of 21 and 28. The GCD of 21 and 28 is 7. Divide both the numerator and the denominator by 7: $\frac{21\div7}{28\div7}=\frac{3}{4}$.

Answer:

$\frac{3}{4}$