Question

question given \\(\sin a = \frac{5}{\sqrt{29}}\\) and that angle \\(a\\) is in quadrant i, find the exact value of \\(\tan a\\) in simplest radical form using a rational denominator. answer attempt 1 out of 2

Explanation:

Step1: Recall sine definition

$\sin A = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{5}{\sqrt{29}}$

Step2: Find adjacent side

Use Pythagorean theorem: $a^2 + 5^2 = (\sqrt{29})^2$
$a^2 + 25 = 29$
$a^2 = 4$
$a = 2$ (Quadrant I, positive)

Step3: Compute tan A

$\tan A = \frac{\text{opposite}}{\text{adjacent}} = \frac{5}{2}$

Answer:

$\frac{5}{2}$