How to Find Sine of any Angle?

Last Updated : 02 Mar, 2024

In a right-angled triangle ABC, where angle A is the angle of interest, and side lengths are denoted as follows:

The sine of angle A (sin A) is calculated as: sin A = $\bold{\frac{a}{c}}$ .

Therefore, to find the sine of any angle A in a right-angled triangle, you can use the formula:

sin A = $\bold{\frac{length of the opposite side}{length of the hypotenuse}}$

Sine of any angle

The sine of any angle in a right-angled triangle can be found using the following formula:

$\sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}}$

For common angles like 30°, 45°, 60°and 90°, exact values of sine are known:

$\bold{\sin(30^\circ) = \frac{1}{2} }$

$\bold{\sin(45^\circ) = \frac{\sqrt{2}}{2}}$

$\bold{\sin(60^\circ) = \frac{\sqrt{3}}{2}}$

$\bold{\sin(90^\circ) = 1 }$

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