Grade 10 — Right Triangles & Trig

Right Triangles & SOH CAH TOA

A **right triangle** is a triangle that contains a $90^\circ$ angle. The sides of a right triangle have special names: the side opposite the right angle is the **hypotenuse**, and the other two sides are **legs**.

For any acute angle $\theta$ in a right triangle, we can define three fundamental trigonometric ratios. A common mnemonic to remember these is **SOH CAH TOA**.

**SOH**: **S**in($\theta$) = **O**pposite / **H**ypotenuse
**CAH**: **C**os($\theta$) = **A**djacent / **H**ypotenuse
**TOA**: **T**an($\theta$) = **O**pposite / **A**djacent

The **Pythagorean Theorem** states that for any right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs: $a^2 + b^2 = c^2$.

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Video: Right Triangle Trig Explained!

Watch this video to visualize the relationships between angles and side lengths in a right triangle! 🎥

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Practice Problems

Use SOH CAH TOA and the Pythagorean Theorem to solve for the missing values. Round to two decimal places if needed.

1) A right triangle has legs of length 3 and 4. What is the length of the hypotenuse?

2) In a right triangle, the opposite side is 5 and the hypotenuse is 13. What is $\sin(\theta)$?

3) The adjacent side is 12 and the hypotenuse is 13. What is $\cos(\theta)$?

4) The opposite side is 5 and the adjacent side is 12. What is $\tan(\theta)$?

⚡ Trig Speed Quiz

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