Question

In right triangle ABC, angle A and angle B are complementary angles. The value of cos A is 5/13. What is the value of sin B?

Answer 1

Since A and B are complementary A+B=90 ans hence A=90-B
COS A =5/13 i.e COS (90-B) = 5/13 i.e
SIN B = 5/13.

Answer 2

sin B Value is $\bold{\frac{5}{13}}$, if the angle A and B are the complementary angles

Given:

$\cos A=\frac{5}{13}$

To find:

The value of sin B

Solution:  

If angle A and Angle B both are complementary angles such that the sum of those two angles are should be 90 degrees.

Such that sum of angle A and angle B = 90 degrees  

$\begin{array}{l}{A+B=90} \\ {A=90-B}\end{array}$

$\cos A=\cos (90-B)=\frac{5}{13} \ldots \ldots \ldots (1)$

$\cos (90-\theta)=\sin \theta$

Therefore, \cos (90-b)=\sin b

Then, from equation (1),

$\cos A=\sin B=\frac{5}{13}$

The value of $\sin B \text { is } \frac{5}{13}$