① Naming the sidesCalculator useful
Name the sides of a right-angled triangle from the marked angle: the hypotenuse is opposite the right angle, the opposite side is across from the marked angle and the adjacent side is next to it.
② Finding a sideCalculator useful
Use SOH CAH TOA. Label the sides, choose the ratio that uses the side you know and the side you want, then rearrange.
③ Finding an angleCalculator useful
Write the ratio of the two sides you know, then use the inverse function (sin⁻¹, cos⁻¹ or tan⁻¹) to find the angle.
④ Using trigonometry to solve problemsCalculator useful
The picture only sets the scene. Draw your own right-angled triangle from it, mark the right angle and the angle you are using, then decide which ratio to use.
⑤ Trigonometry in 3DCalculator usefulExtension
Find a right-angled triangle inside the solid. Drag a diagram to turn it round, or click it and use the arrow keys.
Key steps
SOH CAH TOA: sin = O ÷ H, cos = A ÷ H, tan = O ÷ A.
Label first: the hypotenuse is opposite the right angle; the opposite side is across from the angle you are using; the adjacent side is next to it.
Finding a side: if the unknown is on top, multiply; if it is underneath, divide.
Finding an angle: use sin⁻¹, cos⁻¹ or tan⁻¹ and give the answer to 1 decimal place. Check your calculator is in degree mode.
Rounding: give lengths correct to 3 significant figures and angles to 1 decimal place.