Triangle Height Figurer

Calculate the meridian of a triangle past inbound the base of operations and area dimensions below.

How to Calculate the Peak of a Triangle

Triangle height, as well referred to every bit its altitude, can be solved using a simple formula using the length of the base and the surface area.

h = 2 T b

Thus, the height or altitude of a triangle h is equal to 2 times the expanse T divided by the length of base b.

Diagram of a triangle showing base and height

How to Solve Triangle Height Without the Area

Given the length of the triangle's three sides it is possible to calculate the meridian by offset solving for the area. The surface area of a triangle can exist found using Heron's formula.

The first pace is to find the perimeter of the triangle p, which can exist plant by calculation all iii sides.

p = a + b + c

Then, using the perimeter solve for the semiperimeter due south which is equal to half the perimeter.

s = p 2

Finally, apply the semiperimeter s and the length of 3 sides a, b, and c with Heron's formula to solve the area of a triangle.

T = s(s – a)(s – b)(s – c)

Thus, the surface area T of a triangle is equal to the square root of south times s minus a times s minus b times s minus c .

Then, to solve for height, use the area and the base with the formula above.

How to Solve the Height of a Right Triangle

For a right triangle there is a simple formula to solve the height, which is derived from the Pythagorean theorem.

h = ab c

The altitude h of a correct triangle is equal to a times b, divided by c.

diagram of a right triangle showing legs a and b, hypotenuse c, angles alpha and beta, and height h

How to Solve the Height of an Isosceles Triangle

An isosceles triangle has two heights, the height of base a and the height of base of operations b. Use the following formulas to solve the heights of each.

ha = √(a² – (0.5 × b)²) × b a

The altitude ha of base a is equal to the square root of a squared minus 0.five times b, squared, times b, divided by a.

hb = a² – (0.5 × b)²

The altitude hb of base b is equal to the foursquare root of a squared minus 0.5 times b, squared.

Diagram of an isosceles triangle showing the altitude of base b and side a

How to Solve the Superlative of an Equilateral Triangle

Since an equilateral triangle has three equal sides and three equal angles, information technology also has three equal heights. The formula to find the height of an equilateral triangle is:

h = a × √3 2

The altitude h is equal to a times the foursquare root of 3, divided past 2.

diagram showing the parts of an equilateral triangle

Share triangle height calculator