Question

∠A is an acute angle in a right triangle.

Answer 1

5/ 13 is your answer

Answer 2

Cos A = 12/13

$sin^{2}A$ = $1 - cos^{2}A$

Plug in the value of cos A = 12/13

$sin^{2}A$ = $1 - \left ( \frac{12}{13} \right )^{2}$

$sin^{2}A$ = $1 - \left ( \frac{144}{169} \right )$

$sin^{2}A$ = $\frac{169-144}{169}$

$sin^{2}A$ = $\frac{25}{169}$

Sin A = $\pm$ (5/13)