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Special Right Triangles

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

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Trig Ratios

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Special Right Triangles

Right Triangles and Trigonometry • SAT Math

Set 4 — Mastery

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

$x\sqrt{2}$

$2x$

$\frac{x}{2}$

$\sqrt{2}$

In a 30-60-90 triangle, if the shorter leg is $5$ , what is the length of the longer leg?

$5\sqrt{3}$

$10$

$5$

$15$

What is the ratio of the lengths of the sides of a 30-60-90 triangle?

1 : $\sqrt{3}$ : 2

1 : 1 : 1

1 : 2 : 3

1 : 1 : $\sqrt{2}$

If the hypotenuse of a 45-45-90 triangle is $8\sqrt{2}$ , what is the length of each leg?

$8$

$4\sqrt{2}$

$16$

$2\sqrt{2}$

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

$6$

$4$

$12$

$8$

Which of the following represents the length of the hypotenuse in a 45-45-90 triangle if the legs are each $x$ ?

$x\sqrt{2}$

$2x$

$x^{2}$

$2$

In a 30-60-90 triangle, if the shorter leg is $7$ , what is the hypotenuse?

$14$

$7\sqrt{3}$

$10$

$21$

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

$5\sqrt{3}$

In a 45-45-90 triangle, if the hypotenuse is $12\sqrt{2}$ , what is the length of each leg?

$12$

$6\sqrt{2}$

$24$

$6$

10.

In a 30-60-90 triangle, if the longer leg is $8\sqrt{3}$ , what is the length of the shorter leg?

$8$

$4$

$16$

$12$

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