Question

What special right triangle is shown ??

Answer 1

The triangle shown is a special right triangle 30°-60°-90°.

In this types of triangles the measure of the hypotenuse is two times that of the leg opposite the 30° angle, and the measure of the other leg is sqrt(3) times that of the leg opposite the 30°. This comes from the fact that:

`\begin{gathered} \text{hyp}=opp\sin 30 \\ \text{hyp}=(1)/(2)\text{opp} \\ \text{then} \\ 2\text{hyp}=\text{opp} \end{gathered}`

and:

`\begin{gathered} \text{adj}=\frac{\text{opp}}{\tan 30} \\ \text{adj}=\frac{opp}{\frac{1}{\sqrt[]{3}}} \\ \text{adj}=\sqrt[]{3}opp \end{gathered}`