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Right angled triangle

It is possible to calculate side lengths and angles of a right angled triangle that are not given, if you know some very simple formulas of sine, cosine and tangent.

We have often been asked, why we on this site don’t explain the way to calculate the angle C. The reason for that is obvious: The angle C of a right angled triangle is always 90˚.

Sine


Sine of an angle is equal to the opposite side divided by the hypotenuse. That is:

sin(A)=frac{a}{c}

A=sin^{-1}(frac{a}{c})

sin(B)=frac{b}{c}

B=sin^{-1}(frac{b}{c})

Cosine


Cosine to an angle is equal to the adjacent side divided by the hypotenuse. That is:

cos(A)=frac{b}{c}

A=cos^{-1}(frac{b}{c})

cos(B)=frac{a}{c}

B=cos^{-1}(frac{a}{c})

Tangent


Tangent to an angle is equal to the opposite side divided by the adjacent side. That is:

tan(A)=frac{a}{b}

A=tan^{-1}(frac{a}{b})

tan(B)=frac{b}{a}

B=tan^{-1}(frac{b}{a})

See the list of formulas to the right for more trigonometric formulas.