Isosceles triangle calculator

This calculator calculates any isosceles triangle specified by two of its properties. An isosceles triangle is a triangle where two sides have the same length. To calculate the properties of an isosceles triangle when given certain information, you can use the Pythagorean theorem, the Law of Cosines, or the Law of Sines.

If you know the lengths of two congruent sides (a,a) and the length of the non-congruent side (c) of an isosceles triangle, you can use the Law of Cosines to find the measure of the angles.

The Law of Cosines states that:
c² = a² + a² - 2aa * cos γ

where c is the length of the non-congruent side, a is the length of the congruent sides, and C is the measure of the angle opposite side c. By solving this equation you can find the value of cos γ and then use the inverse cosine function (arccos) to find the measure of angle C in radians or degree.

Additionally, you can use the Law of Sines to find the measure of the angles, the formula is:

sin α = a/c * sin γ

once you find the sine of angle A, you can use the inverse sine function (arcsin) to find the measure of angle A in radians or degree.

You can also use the given sides and angles to find the area of the triangle using Heron's formula or using trigonometric functions like Sin or Cos. (T=12 p=16).

Examples of calculating isosceles triangles:

• Angle α and base c
• base c and arm a
• height and arm a
• area S and Angle γ

An isosceles triangle in word problems in mathematics:

• An isosceles 2
  An isosceles triangular frame has a measure of 72 meters on its legs and 18 meters on its base. Find the perimeter of the frame.
• Identical line
  In which triangles is the line identical with the height?
• Triangle - same sides
  Can the sides of a triangle have lengths of 11, 11, and 14? If so, what kind of triangle is it?
• Isosceles triangle
  Calculate the perimeter of the isosceles triangle with arm length 87 cm and base length of 95 cm.
• Isosceles triangle
  Calculate the area of an isosceles triangle, the base measuring 16 cm and the arms 10 cm.
• Isosceles IV
  In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle.
• Calculation - isosceles
  Calculate the area and perimeter of an isosceles triangle if given: base a: 6cm, height to the base: 4cm.
• Triangle angle calculation
  The outside angle at the base of an isosceles triangle is 132 degrees. Calculate the angles of a triangle internally.
• Right isosceles triangle
  What can be the area of a right isosceles triangle with a side length of 8 cm?
• Isosceles triangle
  Find the area of an isosceles triangle whose leg is twice the base, b=1
• Circumscribed iso triangle
  Construct an isosceles triangle if a given circle circumscribed with a radius r = 2.6 cm is given.
• Isosceles from square
  How many isosceles triangles form in a square when we mark all diagonals?
• Triangle base angle
  An isosceles triangle has an angle of 78°20' at the base. Calculate the size of the angle between the arms.
• Embankment height
  The profile of the railway embankment has the shape of an isosceles trapezoid, where a = 16.4 m, c = 10.6 m, and b = d = 5.2 m. Calculate the embankment height.
• Isosceles trapezium
  Calculate the area of an isosceles trapezium ABCD if a = 10cm, b = 5cm, c = 4cm.

more triangle problems »

Also, take a look at our friend's collection of math problems and questions!

• Isosceles triangle
• triangle
• right triangle
• Heron's formula
• The Law of Sines
• The Law of Cosines
• Pythagorean theorem
• triangle inequality
• similarity of triangles
• The right triangle altitude theorem

See triangle basics on Wikipedia or more details on solving triangles.