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.
• Triangle - same sides
  Can the sides of a triangle have lengths of 11, 11, and 14? If so, what kind of triangle is it?
• Identical line
  In which triangles is the line identical with the height?
• Isosceles triangle
  Find the area of an isosceles triangle whose leg is twice the base, b=1
• Isosceles triangle
  The given is an isosceles triangle with a base of 24dm and an arm of 15dm. Calculate the height of the triangle.
• Iso triangle
  An isosceles triangle with a base of 8 cm. Its circumference is 28 cm. Calculate the height of the triangle.
• Bisector 2
  ABC is an isosceles triangle. While AB=AC, AX is the bisector of the angle ∢BAC meeting side BC at X. Prove that X is the midpoint of BC.

• Length IT
  Find the length (circumference) of an isosceles trapezoid in which the length of the bases a,c, and the height h is given: a = 8 cm c = 2 cm h = 4 cm.
• Isosceles triangle
  Calculate the area of an isosceles triangle, the base measuring 16 cm and the arms 10 cm.
• Calculation - isosceles
  Calculate the area and perimeter of an isosceles triangle if given: base a: 6cm, height to the base: 4cm.
• Isosceles 65784
  An isosceles triangle has an angle of 78°20' at the base. Calculate the size of the angle between the arms.
• Isosceles triangle
  Calculate the perimeter of the isosceles triangle with arm length 87 cm and base length of 95 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.
• Isosceles gable
  The roof of a cottage has a gable in the shape of an isosceles triangle with a base length of 8m and a side length of 10m. How high is the gable?
• Circumscribed iso triangle
  Construct an isosceles triangle if a given circle circumscribed with a radius r = 2.6 cm is given.

more triangle problems »

Look also 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.