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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 1 — Foundation

In a right triangle, if the angle $\theta$ has a sine value of $\frac{3}{5}$ , what is the length of the opposite side if the hypotenuse is 10?

If in a right triangle, the adjacent side is 12 and the angle $\theta$ is such that $\tan(\theta) = \frac{5}{12}$ , what is the length of the opposite side?

In a right triangle, if the cosine of angle $\theta$ is $\frac{4}{5}$ , what is the length of the adjacent side if the hypotenuse is 25?

What is the value of $\sin(30^{\circ})$ ?

$\frac{1}{2}$

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

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

If the opposite side of a right triangle is 7 and the adjacent side is 24, what is $\tan(\theta)$ ?

$\frac{7}{24}$

$\frac{24}{7}$

What is the value of $\cos(60^{\circ})$ ?

$\frac{1}{2}$

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

If the sine of an angle is $\frac{5}{13}$ , what is the cosine of that angle?

$\frac{12}{13}$

$\frac{5}{13}$

$\frac{13}{5}$

In a right triangle, if the opposite side is 9 and the hypotenuse is 15, what is $\sin(\theta)$ ?

$\frac{3}{5}$

$\frac{9}{15}$

$\frac{2}{5}$

$\frac{5}{3}$

What is the value of $\tan(45^{\circ})$ ?

$\sqrt{2}$

$\frac{1}{\sqrt{2}}$

10.

If the opposite side is 8 and the adjacent side is 15, what is $\sin(\theta)$ ?

$\frac{8}{17}$

$\frac{15}{8}$

$\frac{8}{15}$

$\frac{17}{8}$

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