Pythagoras's theorem, SOHCAHTOA, finding side length from angles
The area of a triangle is given by
where b is the base and h is the height.
In a right angled triangle with sides a, b and hypotenuse (longest side) c, Pythagoras' Theorem states
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.
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.
Trigonometric functions can also be used to find an unknown side length in a right triangle:
We know that
Nice work completing Right-angled triangles, here's a quick recap of what we covered:
Exercises checked off
Pythagoras's theorem, SOHCAHTOA, finding side length from angles
The area of a triangle is given by
where b is the base and h is the height.
In a right angled triangle with sides a, b and hypotenuse (longest side) c, Pythagoras' Theorem states
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.
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.
Trigonometric functions can also be used to find an unknown side length in a right triangle:
We know that
Nice work completing Right-angled triangles, here's a quick recap of what we covered:
Exercises checked off