Question

tan z
what is the correct ratio?
(right triangle with right angle at i, sides: iz = 24, ix = 7, zx = 25)
options: 7/25, 24/25, 7/24, 24/7

Explanation:

Step1: Recall tangent definition

For an acute angle in a right triangle, $\tan(\theta) = \frac{\text{opposite side}}{\text{adjacent side}}$

Step2: Identify sides for $\angle Z$

Opposite side to $\angle Z$: $XY = 7$; Adjacent side to $\angle Z$: $YZ = 24$

Step3: Calculate $\tan Z$

$\tan Z = \frac{7}{24}$

Answer:

$\frac{7}{24}$ (matches the orange card option)