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Right-angled trigonometry
Pythagoras links three sides. Trigonometry links sides and angles. The word SOHCAHTOA holds all three rules.
Label the sides
Stand at the angle you are using.
Hypotenuse (H): opposite the right angle.
Opposite (O): across from your angle.
Adjacent (A): next to your angle, but not the hypotenuse.
Hypotenuse (H): opposite the right angle.
Opposite (O): across from your angle.
Adjacent (A): next to your angle, but not the hypotenuse.
SOHCAHTOA
sin θ = OH cos θ = AH tan θ = OA
Pick the ratio that uses the two sides in the question: the one you know and the one you want.
Pick the ratio that uses the two sides in the question: the one you know and the one you want.
Missing side or missing angle
Missing side: put in the numbers and rearrange. x = 12 × sin 35°
Missing angle: use the inverse button. θ = sin-1(59)
Missing angle: use the inverse button. θ = sin-1(59)
The hypotenuse is 12 cm and the angle is 35°. Find the side opposite the angle.
- You know H and want O, so use SOH: sin 35° = x12
- Multiply both sides by 12: x = 12 × sin 35°
- Calculator: x = 6.882... = 6.88 cm (3 s.f.)
Answer: 6.88 cm
Label O, A, H from your angle. Choose sin, cos or tan from SOHCAHTOA using the two sides involved. Use inverse functions to find an angle.
The interactive lesson includes the diagrams for this topic.
Check you have got it
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