Foundation and Higher · trigonometry

SOH CAH TOA
in four steps.
Sides and angles.

it all starts with
labelling the sides

first, the word itself —

Trigonometry

tri · gon · metry

three · angle · measure

step 1 of 4

Label the sides

Hypotenuse: opposite the right angle.

Opposite: straight across from your angle.

Adjacent: next to your angle.

✓ Always label from the angle
you are using

step 2 of 4

Pick the ratio

1. You have the hypotenuse.
You want the opposite.

2. O and H sit together in SOH.

✓ Use sin: sin = opposite ÷ hypotenuse

step 3 of 4

Find the side

1. Write it down: sin 35° = x ÷ 12.

2. Multiply both sides by 12:
x = 12 × sin 35°.

✓ x = 6.88 cm (3 s.f.)

step 4 of 4

Find an angle

1. You have O and A: that is TOA.
tan θ = 7 ÷ 10 = 0.7

2. To undo tan, press shift tan: tan⁻¹.

✓ θ = tan⁻¹(0.7) = 35.0°

the three ratios —

SOH

sin = opposite ÷ hypotenuse

CAH

cos = adjacent ÷ hypotenuse

TOA

tan = opposite ÷ adjacent

Missing side: sin, cos, tan.
Missing angle: press shift first.

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