In a right-angled triangle, name the sides from the angle you are using, θ. The hypotenuse is opposite the right angle. The opposite side is across from θ. The adjacent side is next to θ, but is not the hypotenuse.
The three ratios are sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse and tan θ = opposite/adjacent. Many people remember them as SOH CAH TOA. To choose, look at which two sides the question involves: the one you know and the one you want.
Worked example
In triangle ABC, ∠B = 90°, ∠A = 25° and AB = 8 cm. Which ratio finds BC?
- From A: AB is adjacent and BC is opposite.
- Opposite and adjacent go with tangent.
Answer:tan 25° = BC/8
Key words
- hypotenuse
- the side opposite the right angle
- opposite
- the side across from the angle
- adjacent
- the side next to the angle
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New questions every time.
Common Core-referenced: HSG-SRT.C.6