Use right triangle trigonometry (sin, cos, tan) to solve for sides/angles. | Right triangles and trigonometry | SAT Math

Match the angle first, then choose sine, cosine, or tangent from the side ratio.

核心知识

SOH-CAH-TOA: $s i n 𝜃 = o p p o s i t e h y p o t e n u s e$ , $c o s 𝜃 = a d j a c e n t h y p o t e n u s e$ , $t a n 𝜃 = o p p o s i t e a d j a c e n t$ . Pick the ratio that connects the side you know to the side you need.

深入理解

SOH-CAH-TOA tells you which ratio connects the side you know to the side you need.

Sine uses opposite over hypotenuse.
Cosine uses adjacent over hypotenuse.
Tangent uses opposite over adjacent.

Label the sides from the angle in the problem, not from the angle you wish you had.

分步讲解

Identify the acute angle you'll work with.
Label the sides as opposite, adjacent, and hypotenuse relative to that angle.
Pick the trig ratio that connects the known side to the unknown side.
Set up the equation and solve: $u n k n o w n = k n o w n \times (t r i g v a l u e)$ or $u n k n o w n = k n o w n t r i g v a l u e$ .

常见误解

Labeling sides relative to the wrong angle — always use the angle named in the problem.
Using sine when you need cosine (or vice versa) because the sides are mislabeled.
Forgetting that the hypotenuse is always the longest side and is never "opposite" or "adjacent" in the ratio denominator context — it's always in a specific position.

题目

示例解析

In right triangle $𝑃 𝑄 𝑅$ , angle $𝑃$ is a right angle, $s i n 𝑄 = 45$ , and $𝑃 𝑅 = 12$ . What is the length of $𝑄 𝑅$ ?

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