How to Find Angles Using Sine

The sine of an angle is the ratio of the length of the opposite side divided by the hypotenuse. This can be seen using the following right triangle. The right triangle ABC has side (a) which is opposite angle A, side (b) opposite angle B and side (c) which is the hypotenuse and opposite angle C. Therefore the sine of an angle using a right triangle is sine A=side a / c. We use this formula to solve for all the angles in this right triangle ABC.

Things You'll Need

• Scientific calculator

Instructions

1. Use the right triangle for the following values: a=3 b=4 and c=5. The sine of A= a/c

2. Plug in the values for a and c.

3. Calculate the value of a/c with the calculator, which is 3/5. The value of a/c=3/5= .60 degrees is the value of sine angle A.

4. The final angle is angle B, which is the sine B= b/c. There is no need to solve for angle C since this is a right triangle.

5. Plug in the values for b and c. 4/5=.8= sine B

References

• Clark University: The Relation Between Sines and Chords