Triangle formulas

List of triangle formulas used to calculate angles, sides, height, area and perimter of a triangle.

triangle altitude from each angle

Law of sines

a = b = c
sin A sin B sin C

The law of sines can be used to calculate the remaining sides of a triangle when two angles and a side are known or two sides and one of the non-enclosed angles are known.

Law of cosines

c2 = a2 + b2 - 2ab cos(angle C)

The law of cosines can be used to calculate the third side of a triangle when two sides and their enclosed angle are known or if all three sides are known.

Pythagorean theorem

a2 + b2 = c2

The Pythagorean theorem can only be used with right-angled triangles: if the lengths of any two sides are known the length of the third side can be calculated.

Sum of three angles

angle A + angle B + angle C = 180o

If two angles are know, the third angle can be calculated.

Triangle formulas to calculate the height from each angle

hc = a * sin(angle B) or
hc = b * sin(angle A)

hb = a * sin(angle C) or
hb = c * sin(angle A)

ha = b * sin(angle C) or
ha = c * sin(angle B)

Formula to calculate the area of a triangle

Area triangle = (BASE x HEIGHT)/2

Formula to calculate the perimeter of a triangle

Perimeter triangle = side a + side b + side c