Special Right Triangles (Set 2) Worksheet

Sample problems

Use the special-triangle ratios. In a $45^{\circ }$-$45^{\circ }$-$90^{\circ }$ triangle the legs are equal and the hypotenuse is a leg times $\sqrt{2}$. In a $30^{\circ }$-$60^{\circ }$-$90^{\circ }$ triangle, with $s$ the short leg (opposite $30^{\circ }$): the long leg is $s\sqrt{3}$ and the hypotenuse is $2s$. Give every answer in exact simplest-radical form.

1. 1. Find the length of the hypotenuse $x$ of this $45^{\circ }$-$45^{\circ }$-$90^{\circ }$ triangle.
2. 2. A $45^{\circ }$-$45^{\circ }$-$90^{\circ }$ triangle has legs of length $12$. Find the length of its hypotenuse.
3. 3. The hypotenuse of a $45^{\circ }$-$45^{\circ }$-$90^{\circ }$ triangle is $14$. Find the length of each leg in simplest radical form.
4. 4. In this $30^{\circ }$-$60^{\circ }$-$90^{\circ }$ triangle the short leg is $5$. Find the long leg $x$ and the hypotenuse $y$.

Plus 10 more problems and a full answer key in the PDF.