Week 17 – Sine Law

This week in pre-calc I learned how to use the sine law for triangles. This can be used when your triangle isn’t a right triangle, there needs to be an angle and on the side across from that angle, a side length and another side or angle given. If there isn’t these 3 clues, then you can’t use the sine law to solve your triangle for the missing side or angles.

When you have your triangle, for example <ABC, angle A, the side across from that is side a, across from angle B is side b and angle C is side c. The sine law is very easy. When solving for a missing side, you put side a on top and it’s being divided by angle A this is equal to side b divided by angle B and thats equal to side c divided by angle C. For a missing angle, the angle is on top and the side length is on the bottom. All the fractions are equal to each other so out of the 3 possible fractions, you only need to use 2, a left side equal to a right side.

With the sine law, you use the hints they give you, the angle with the side length and another clue. When you fill in the missing sides and angles, you can see which 2 fractions you need to use. From there, you need to isolate the variable by itself so the whole equation is trying to solve for that missing value. If the 3rd clue given is another angle, you can simply add the 2 angles together and subtract them form 180 because all triangles have to add up to 180 degrees.