GKT101: General Knowledge for Teachers – Math

1. Find the ratios between the three sides of any $30-60-90$ triangle.

[Figure 4]

The three sides of any 30-60-90 triangle will be in this ratio: $1: \sqrt{3}: 2$.

2. Find the missing sides of the triangle below.

[Figure 5]

The side opposite the $30^{\circ}$ angle is the smallest side because $30^{\circ}$ is the smallest angle. Therefore, the length of $10$ corresponds to the length of $1$ in the ratio $1: \sqrt{3}: 2$. The scale factor is $10$. The other sides of the triangle will be $10 \sqrt{3}$ and $20$, because $10: 10 \sqrt{3}: 20$ is equivalent to $1: \sqrt{3}: 2$. $B C=10 \sqrt{3}$ and $A C=20$.