Question

find: tan a

Explanation:

Step1: Recall tangent definition

In a right triangle, $\tan\theta = \frac{\text{opposite}}{\text{adjacent}}$ to $\theta$.

Step2: Identify sides for $\angle A$

For $\angle A$, opposite side is $BC$ (let's find its length: using Pythagoras, $BC = \sqrt{5^2 - 4^2} = 3$), adjacent side is $AB = 4$.

Step3: Calculate $\tan A$

$\tan A = \frac{BC}{AB} = \frac{3}{4}$.

Answer:

$\frac{3}{4}$