Question

find the ratio for tan ∠t

Explanation:

Step1: Recall the tangent ratio

In a right triangle, the tangent of an acute angle is the ratio of the length of the opposite side to the length of the adjacent side. For $\angle T$, we need to identify the opposite and adjacent sides.

Step2: Identify sides relative to $\angle T$

In right triangle $TAC$ (with right angle at $A$), for $\angle T$:

• The side opposite $\angle T$ is $AC$, which has length $7$.
• The side adjacent to $\angle T$ is $TA$, which has length $24$.

Step3: Calculate $\tan(\angle T)$

Using the tangent ratio formula $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$, we substitute the lengths:
$\tan(\angle T)=\frac{AC}{TA}=\frac{7}{24}$

Answer:

$\frac{7}{24}$ (corresponding to the option with $7/24$)