Question

If sin A = `5/13` the value of tan A is ______.

Options

• `5/12`

• `12/13`

• `12/5`

• `13/12`

Answer 1

If sin A = `5/13` the value of tan A is `bbunderline(5/12)`.

Explanation:

Given \[\sin A = \frac{\text{Perpendicular}}{\text{Hypotenuse}} = \frac{5}{13}\], we find the base using the Pythagorean theorem: \[\text{Base} = \sqrt{13^2 - 5^2} = \sqrt{169 - 25} = \sqrt{144} = 12\]. The value of tan A is \[\frac{\text{Perpendicular}}{\text{Base}} = \frac{5}{12}\].