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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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Trigonometry Ratios

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Special Right Triangles

Trigonometry Destroyer • SAT Math Destroyer Crash Course

Set 1 — Mastery

In a 30-60-90 triangle, if the shortest side measures $5$ , what is the length of the hypotenuse?

$10$

$5\sqrt{3}$

$5\sqrt{2}$

$15$

What is the length of the longer leg of a 45-45-90 triangle if the length of each leg is $x$ ?

$x$

$x\sqrt{2}$

$2x$

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

If a 30-60-90 triangle has a hypotenuse of $12$ , what is the length of the shorter leg?

$6$

$4$

$12$

$2\sqrt{3}$

In a 45-45-90 triangle, if the hypotenuse is $10$ , what is the length of each leg?

$5$

$10\sqrt{2}$

$5\sqrt{2}$

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

A 30-60-90 triangle has a longer leg measuring $8$ . What is the length of the shorter leg?

$4$

$8\sqrt{3}$

$4\sqrt{3}$

$\frac{8}{\sqrt{3}}$

If the legs of a 45-45-90 triangle each measure $x$ , what is the hypotenuse in terms of $x$ ?

$x$

$x\sqrt{2}$

$2x$

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

In a 30-60-90 triangle, if the longer leg is $10$ , what is the length of the hypotenuse?

$10\sqrt{3}$

$20$

$15$

$5\sqrt{3}$

What is the ratio of the lengths of the sides in a 45-45-90 triangle?

$1:1:\sqrt{2}$

$1:1:1$

$1:2:1$

$1:1:2$

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

$\frac{x}{2}$

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

$x\sqrt{3}$

$x$

10.

If the legs of a 30-60-90 triangle measure $a$ and $b$ respectively, and $b$ is the longer leg, what is the relationship between $a$ and $b$ ?

$b = a\sqrt{3}$

$b = 2a$

$b = a^{2}$

$b = \frac{a}{\sqrt{3}}$

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