# Isosceles Triangle Angles Calculator

Created by Rijk de Wet
Reviewed by Krishna Nelaturu
Last updated: Mar 06, 2024

Welcome to the isosceles triangle angles calculator, where we'll show you how to calculate the angles of an isosceles triangle. Along the way, we hope to teach you more about:

• What kinds of angles an isosceles triangle has;
• What the vertex angle of an isosceles triangle is; and
• What angles an isosceles right triangle has.

## How do I use the isosceles triangle angles calculator?

The isosceles triangle angles calculator gets to the point without cutting any triangles' corners. Here's how to use it:

1. Enter the length of your triangle's legs and the base length ($a$ and $b$, respectively). If you need to enter the value in a different unit, click on the unit to change it, then enter the length.

2. See how the calculator instantly works out the vertex angle and base angles ($\beta$ and $\alpha$). If you desire the result in a different unit, you can change it by clicking on the unit.

For example, consider an isosceles triangle with 4 cm legs and a 5 cm base. Enter the legs and base length in our calculator. Right away, it tells you that the vertex angle $\beta = 77.4\degree$, and the base angle $\alpha = 51.3\degree$.

The calculator can work backward, too! Try inputting your mystery triangle's angles with one side's length (the isosceles triangle angles calculator needs some sense of proportion) and see how it works out the remaining side's length.

Say you want to calculate the legs of a right isosceles triangle whose hypotenuse (base) is 12 feet long. Here, you enter the vertex angle $\beta = 90\degree$. Next, click on the base's unit and change it to feet. Enter the base length $b = 12\rm\ ft$. Instantly, you can learn that the legs are 8.49 ft each.

If you still want to learn what an isosceles triangle is and how to calculate its angles, read on!

## What is an isosceles triangle? What kind of angles does an isosceles triangle have?

An isosceles triangle is a triangle with two sides of equal length. We usually call these two sides the "legs" ($a$ below) and the remaining side the "base" ($b$).

Because the legs of an isosceles triangle are the same length, the two angles they form with the base are also equal. We call the angles adjacent to the base side the base angles ($\alpha$) and the remaining angle the vertex angle ($\beta$).

## How do I find the angles of an isosceles triangle?

Finding the angles $\alpha$ and $\beta$ of an isosceles triangle is easy — all you need is some geometry tricks!

1. Find $a$ and $b$, the length of the isosceles triangle's base and legs.
2. Split the isosceles triangle down its axis of symmetry (i.e. from its vertex angle straight down the middle of the base) to obtain two mirrored right triangles.
3. Use trigonometry to work out the angles, which will be $90^\circ$, $\alpha$, and $\beta/2$.

## What is an isosceles right triangle?

An isosceles right triangle is the child of a right triangle and an isosceles triangle, and so it has all of its parents' attributes. It has two equal sides and one angle (in this case, the vertex angle) that is $90^\circ$. The two base angles are then $45^\circ$ each.

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## Meet the creator of isosceles triangle angles calculator

I'm Rijk, a data scientist and an expert at creating scientific tools. Through rigorous user data analysis, I found people had difficulty calculating isosceles triangle angles and immediately created a solution. Ever since, this calculator has helped numerous people, and I hope you had fun using it, too!

We put extra care into the quality of our content so that they are as accurate and reliable as possible. Each tool is peer-reviewed by a trained expert and then proofread by a native speaker. You can learn more about our standards on our page.

## FAQ

### What is the vertex angle of an isosceles triangle?

The vertex angle of an isosceles triangle is the angle formed by the triangle's two legs (the two sides that are of equal length). It is unique in the triangle unless all three sides are equal and the triangle is equilateral.

### Can an isosceles triangle have a 90 degree angle?

Yes — an isosceles triangle can have a 90-degree angle. This angle would be its vertex angle. We can call an isosceles triangle with a 90-degree angle a right isosceles triangle. The base angles of an isosceles triangle can't be 90 degrees — a shape with two or more 90° angles can't even be a triangle at all!

### What are the angles of an isosceles triangle with a vertex angle of 90°?

If an isosceles triangle has a vertex angle β = 90°, we only need to calculate one more angle — the base angle, α, which features twice.

1. The sum of a triangle's angles is 180°, i.e.:
2α + β = 180°.
2. Make α the subject of the equation:
α = (180° − β) / 2
3. Substitute β = 90°:
α = (180° − 90°) / 2
4. Work out the equation to obtain α = 45°.
Rijk de Wet
Leg (a)
in
Base (b)
in
Vertex angle (β)
deg
Base angle (α)
deg
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