Question

find the exact value of tan a in simplest radical form.

Explanation:

Step1: Recall the definition of tangent in a right triangle

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 \( A \), the opposite side is \( BC \) and the adjacent side is \( AC \).

Step2: Identify the lengths of the opposite and adjacent sides

From the triangle, \( BC = 24 \) (opposite to angle \( A \)) and \( AC = 7 \) (adjacent to angle \( A \)).

Step3: Calculate \( \tan A \)

Using the definition of tangent, \( \tan A=\frac{\text{opposite}}{\text{adjacent}}=\frac{BC}{AC} \). Substituting the values, we get \( \tan A = \frac{24}{7} \).

Answer:

\( \frac{24}{7} \)