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Trigonometry Ratios

This worksheet covers Trigonometry Ratios, 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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Related Lessons:

Special Right Triangles

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Trigonometry Ratios

Trigonometry Destroyer • SAT Math Destroyer Crash Course

Set 1 — Mastery

In a right triangle, if the length of the opposite side is $6$ and the length of the hypotenuse is $10$ , what is the value of $\sin(\theta)$ ?

$0.6$

$0.8$

$0.5$

$0.4$

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

$\frac{4}{5}$

$\frac{3}{5}$

$\frac{1}{5}$

$\frac{2}{5}$

In a triangle, if $\tan(\alpha) = 2$ , what is the ratio of the opposite side to the adjacent side?

$1$

$2$

$3$

$4$

A ladder leans against a wall at an angle of $30^\circ$ . If the foot of the ladder is $4$ meters from the wall, what is the length of the ladder?

$4$

$8$

$\frac{4}{\cos(30^\circ)}$

$\frac{4\sqrt{3}}{3}$

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

$13$

$12$

$15$

$20$

What is the value of $\sec(45^\circ)$ ?

$1$

$\sqrt{2}$

$2$

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

In a unit circle, if the angle $\theta$ corresponds to the point $(\frac{1}{2}, y)$ , what is the value of $y$ ?

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

$\frac{1}{2}$

$\sqrt{2}$

$0$

If the angle of elevation from a point $P$ to the top of a tower is $60^\circ$ and the distance from point $P$ to the base of the tower is $10$ m, what is the height of the tower?

$5\sqrt{3}$

$10$

$10\sqrt{3}$

$20$

What is the value of $\cot(30^\circ)$ ?

$\sqrt{3}$

$\frac{1}{\sqrt{3}}$

$1$

$2$

10.

In a right triangle, if the adjacent side is $12$ and the hypotenuse is $13$ , what is $\cos(\theta)$ ?

$\frac{5}{13}$

$\frac{12}{13}$

$\frac{13}{12}$

$\frac{1}{13}$

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