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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 3 — Mastery

In a 30-60-90 triangle, if the length of the side opposite the 30-degree angle is $5$ , what is the length of the hypotenuse?

$10$

$5\sqrt{3}$

$5$

$15$

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

$1:1:\sqrt{2}$

$1:2:1$

$\sqrt{2}:\sqrt{2}:1$

$1:\sqrt{2}:1$

If one leg of a 30-60-90 triangle is $12$ , what is the length of the leg opposite the 60-degree angle?

$12\sqrt{3}$

$6\sqrt{3}$

$12$

$10$

In a 45-45-90 triangle, if the hypotenuse is $10\sqrt{2}$ , what is the length of each leg?

$5$

$10$

$10\sqrt{2}$

$10$

If the hypotenuse of a 30-60-90 triangle is $18$ , what is the length of the side opposite the 30-degree angle?

$9$

$6$

$18$

$12$

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

$x\sqrt{2}$

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

$\sqrt{x}$

$2x$

A ladder makes a $30$ degree angle with the ground and reaches a height of $12$ feet. What is the length of the ladder?

$12\sqrt{3}$

$24$

$14$

$12$

In a 30-60-90 triangle, if the side opposite the 60-degree angle is $x$ , what is the expression for the hypotenuse?

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

$2x$

$\frac{x}{2}$

$x\sqrt{3}$

What is the area of a 45-45-90 triangle with legs of length $7$ ?

$24.5$

$49$

$24.5\sqrt{2}$

$49\sqrt{2}$

10.

If the hypotenuse of a 30-60-90 triangle is $24$ , what is the length of the leg opposite the 30-degree angle?

$12$

$24$

$6$

$18$

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