Right angled triangles
Pythagoras's theorem, SOHCAHTOA, finding side length from angles
Want a deeper conceptual understanding? Try our interactive lesson!
Area of triangle equals ½bh
The area of a triangle is given by
where b is the base and h is the height.
Pythagoras' Theorem
In a right angled triangle with sides a, b and hypotenuse (longest side) c, Pythagoras' Theorem states
Trigonometric Ratios
In a right angled triangle with an angle θ<90°, the trigonometric ratios sin, cos and tan are defined by
where opposite and adjacent refer to the side lengths of the sides opposite and adjacent to θ, while hypotenuse is the length of the longest side.
Finding angles in right angled triangles
If we know the value of sinθ, cosθ or tanθ in a right angled triangle, we can find θ using an inverse trigonometric function on a calculator. These functions are sin−1, cos−1 and tan−1 and satisfy
whenever θ<90°, which is always true in a right angled triangle.
Finding side lengths from an angle
The trigonometric ratios sin, cos and tan are actually functions that relate an angle θ to a ratio of sides. The values of sin, cos and tan for specific angles can be found on the calculator. For example
Nice work completing Right angled triangles, here's a quick recap of what we covered:
Skills covered
Exercises checked off