Pythagoras' theorem
In a right-angled triangle, the square on the hypotenuse equals the sum of the squares on the other two sides: . Add the squares to find the hypotenuse; subtract to find a shorter side.
≈ 25 minRight-angled trigonometry
Label the sides opposite, adjacent and hypotenuse relative to the angle. Then SOHCAHTOA tells you which ratio links the two sides you know (or want). Use the ratio to find a side, or the inverse function to find an angle.
≈ 35 minSine rule, cosine rule and area
For triangles without a right angle: use the sine rule when you know a side and its opposite angle, and the cosine rule when you know two sides and the angle between them, or all three sides. The area is .
≈ 40 minTrigonometry in three dimensions
Every 3D problem is a chain of 2D right-angled triangles. Find a triangle on the base first (often a diagonal), then stand a vertical triangle on it. The angle between a line and a plane is the angle between the line and its shadow on the plane.
≈ 35 min