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📐 Trigonometry Basics

Unlock the link between angles and sides in right triangles. Learn SOH-CAH-TOA and use sine, cosine, and tangent to work with the sides you can't reach.

lessons

~15 min

to learn

🔢 Math

subject

Teens

level

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What you’ll learn

Labeling Sides and the Three RatiosLabel a right triangle's sides relative to an angle and state the sine, cosine, and tangent ratios.Trigonometry links a right triangle's angles to its side lengths. From a chosen angle θ, the hypotenuse is the longest side (opposite the right angle), the opposite is across from θ, and the adjacent is beside it. Three ratios follow, captured by SOH-CAH-TOA: sine = opposite/hypotenuse, cosine = adjacent/hypotenuse, and tangent = opposite/adjacent.
Using SOH-CAH-TOAChoose the correct trig ratio and calculate sine, cosine, and tangent values.To use trigonometry, pick the ratio that involves the sides you have: opposite and hypotenuse means sine, adjacent and hypotenuse means cosine, opposite and adjacent means tangent. In a 3-4-5 triangle, sin θ = 0.6, cos θ = 0.8, and tan θ = 0.75, and these values hold for that angle at any size. Trigonometry lets us measure heights, navigate, and even reach the stars.

Questions this course answers

Relative to a chosen angle θ, which side is the 'opposite'?

The opposite side is the one directly across from the angle θ you are focusing on.

Which ratio does 'CAH' describe?

CAH means Cosine = Adjacent ÷ Hypotenuse.

In a 3-4-5 triangle with opposite 3, adjacent 4, hypotenuse 5, what is tan θ?

tan θ = opposite ÷ adjacent = 3 ÷ 4 = 0.75.

You know the adjacent side and the hypotenuse. Which ratio should you use?

Adjacent and hypotenuse together are the cosine ratio (CAH).

A right triangle has opposite 6 and hypotenuse 10. What is sin θ?

sin θ = opposite ÷ hypotenuse = 6 ÷ 10 = 0.6.

Grounded in trusted sources

Khan Academy — right triangle trigonometry
National Council of Teachers of Mathematics
BBC Bitesize — trigonometry
Britannica — trigonometry

Every Wunder lesson is built from real, reputable sources — never invented.

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