# Isosceles triangle calculator

Please enter two properties of the isosceles triangle

Use symbols: a,b c, h, T, p, A, B, C, r, R

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:

c

^{2}= a

^{2}+ a

^{2}- 2aa * cos(C)

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(C) 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(A) = a/c * sin(C)

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:

### An isosceles triangle in word problems in mathematics:

- 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 triangle

Calculate the perimeter of the isosceles triangle with arm length 87 cm and base length of 95 cm. - 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. - Circumscribed 29561

Construct an isosceles triangle if a given circle circumscribed with a radius r = 2.6 cm is given. - Isosceles triangle

Calculate the area of an isosceles triangle, the base measuring 16 cm and the arms 10 cm. - QuizQ

An isosceles triangle has two sides of length 7 km and 39 km. How long is a third side? - 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. - Iso triangle

An isosceles triangle with a base of 8 cm. Its circumference is 28 cm. Calculate the height of the triangle. - Calculate 35411

The given is an isosceles triangle with a base of 24dm and an arm of 15dm. Calculate the height of the triangle. - Isosceles 5856

How many isosceles triangles form in a square when we mark all diagonals? - Isosceles triangle

What are the angles of an isosceles triangle ABC if its base is long a=5 m and has an arm b=4 m? - Embankment 2539

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. - Base

Compute the base of an isosceles triangle, with the arm a=20 cm and a height above the base h=10 cm. - Calculate 3292

The perimeter of the isosceles triangle is 32 cm. The base is 2 cm longer than the shoulder. Calculate the sides 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.

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#### 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