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Trig Ratios

This worksheet covers Trig Ratios, 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

Right Triangles and Trigonometry • SAT Math

Set 5 — Mastery

In a right triangle, if one of the angles is $30^\circ$ and the hypotenuse is 10, what is the length of the side opposite the $30^\circ$ angle?

$5\sqrt{3}$

If $\tan(\theta) = 3$ and $\theta$ is an angle in a right triangle, what is the length of the opposite side if the length of the adjacent side is 4?

In a right triangle, if the lengths of the two legs are 6 and 8, what is the value of $\sin(\theta)$ where $\theta$ is the angle opposite the side of length 6?

$\frac{3}{5}$

$\frac{6}{10}$

$\frac{6}{8}$

$\frac{4}{5}$

If $\sec(\theta) = \frac{5}{3}$ , what is $\cos(\theta)$ ?

$\frac{3}{5}$

$\frac{5}{3}$

$\frac{1}{3}$

$\frac{3}{2}$

In a right triangle, if $\sin(\theta) = \frac{4}{5}$ , what is $\cos(\theta)$ ?

$\frac{3}{5}$

$\frac{4}{5}$

$\frac{5}{4}$

$\frac{1}{5}$

If the opposite side of a right triangle is 7 and the hypotenuse is 25, what is $\sin(\theta)$ ?

$\frac{7}{25}$

$\frac{25}{7}$

$\frac{24}{25}$

$\frac{7}{24}$

In a right triangle, if $\tan(\theta) = 2$ and the adjacent side is 5, what is the length of the opposite side?

If $\cos(\theta) = \frac{12}{13}$ , what is $\sin(\theta)$ ?

$\frac{5}{13}$

$\frac{12}{13}$

$\frac{13}{12}$

$\frac{1}{13}$

In a right triangle, if $\cot(\theta) = 4$ , what is $\tan(\theta)$ ?

$\frac{1}{4}$

0.25

10.

If the lengths of the legs of a right triangle are 9 and 12, what is $\tan(\theta)$ where $\theta$ is the angle opposite the leg of length 9?

$\frac{9}{12}$

$\frac{12}{9}$

$\frac{3}{4}$

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