Special Right Triangles: 45-45-90 and 30-60-90

4 5^{\circ} - 4 5^{\circ} - 9 0^{\circ} : x, x, x 2

3 0^{\circ} - 6 0^{\circ} - 9 0^{\circ} : x, x 3, 2 x

Worked examples

Hypotenuse $= 52$

Long leg $= 43$

Hypotenuse $= 2 (4) = 8$

Putting $x 3$ across from the $3 0^{\circ}$ angle.

The shortest side is across from the smallest angle. So $x$ goes across from $3 0^{\circ}$ , and $x 3$ goes across from $6 0^{\circ}$ .

A 45-45-90 triangle has a leg of 7. Find the hypotenuse.
Show answer
$72$
A 30-60-90 triangle has a hypotenuse of 10. Find both legs.
Show answer
$5$ and $53$
A 45-45-90 triangle has a hypotenuse of $62$ . Find a leg.
Show answer
$6$

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