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Right angled triangles
Pythagoras's theorem, SOHCAHTOA, finding side length from angles
Pythagoras's theorem, SOHCAHTOA, finding side length from angles
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The area of a triangle is given by
where b is the base and h is the height.
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In a right angled triangle with sides a, b and hypotenuse (longest side) c, Pythagoras' Theorem states
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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.
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