Exploring Sine Law

Grade 10s today had a look at relationships in triangles. We measured sides and angles as accurately as we could, and then we looked at ratios.

We compared the ratios of sinA/a and cosA/a and tanA/a and the same for B and C. We noticed a lot of things when we looked at the values.

we noticed that tangent is the only ratio that can have values greater than 1. We looked at why that could be the case. Sine and cosine are ratios of opposite and hypotenuse, and adjacent and hypotenuse. The hypotenuse (always the longest side) is always the denominator, so the fraction will be between 0 and 1 when divided. Tangent compares opposite and adjacent, and sometimes the adjacent is the big side, and sometimes the opposite is the big side, so tangent can be any value from 0 to infinity.

We also noticed that the ratios of sinA/a=sinB/b=sinC/c, and we formalized that this is the sine law. We then started using it to solve problems with non-right angle triangles.