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Special Right Triangles

This worksheet covers Special Right Triangles, which is part of the Trigonometry Destroyer module in the SAT Math Destroyer Crash Course course. Practice problems are designed to strengthen key concepts and build confidence.

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Related Lessons:

Trigonometry Ratios

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Special Right Triangles

Trigonometry Destroyer • SAT Math Destroyer Crash Course

Set 2 — Mastery

In a 45-45-90 triangle, if the length of one leg is $x$ , what is the length of the hypotenuse?

$x \sqrt{2}$

$2x$

$x$

$\frac{x}{\sqrt{2}}$

A 30-60-90 triangle has a shorter leg measuring $5$ units. What is the length of the longer leg?

$5\sqrt{3}$

$10$

$5$

$\frac{5\sqrt{3}}{2}$

Find the area of a 45-45-90 triangle with legs of length $6$ units.

$18$

$36$

$12$

$24$

In a 30-60-90 triangle, if the hypotenuse is $12$ units, what is the length of the shorter leg?

$6$

$12$

$4$

$8$

What is the length of the hypotenuse of a 45-45-90 triangle with legs measuring $x$ ?

$x$

$x \sqrt{2}$

$2x$

$\frac{x}{\sqrt{2}}$

If a 30-60-90 triangle has a shorter leg of length $4$ , what is the length of the hypotenuse?

$8$

$4\sqrt{3}$

$6$

$4$

What is the ratio of the longer leg to the shorter leg in a 30-60-90 triangle?

$\sqrt{3}:1$

$1:1$

$1:2$

$2:1$

A 45-45-90 triangle has a hypotenuse of length $10$ . What is the length of each leg?

$5\sqrt{2}$

$10$

$5$

$\frac{10}{\sqrt{2}}$

If the length of the longer leg in a 30-60-90 triangle is $8$ , what is the length of the hypotenuse?

$16$

$8\sqrt{3}$

$12$

$8$

10.

What is the perimeter of a 30-60-90 triangle with a shorter leg of $3$ units?

$9 + 3\sqrt{3}$

$6 + 3\sqrt{3}$

$9$

$3 + 3\sqrt{3}$

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