Mastering Right‑Triangle Trigonometry: Key Concepts & Formulas

A right triangle contains exactly one right angle (90°).
Trigonometric Identities

In the standard notation, the hypotenuse (H) is always opposite the right angle. For a given acute angle x, the side opposite x is denoted O, and the side adjacent to x is A.
Inverse trigonometric functions—arcsin, arccos, and arctan—return an angle from a ratio input. For instance, since tan 45° = 1, arctan 1 equals 45°.
These “arc” functions are indispensable for determining angles in a right triangle when side lengths are known.
The Pythagorean Theorem

According to standard geometry textbooks, the Pythagorean theorem states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: H² = O² + A².
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