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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