Isosceles Triangle Angles Calculator

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.

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).
2. See how the calculator works out the vertex angle and base angles ($\beta$ and $\alpha$).
3. The calculator can work backward, too! Try inputting your mystery triangle's angles together 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.

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

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 ($\beta$).

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 $\beta/2$.

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.

If you found this isosceles triangle angles calculator handy, you may also like:

• Isosceles triangle;
• Isosceles right triangle;
• Isosceles triangle find A;
• Isosceles triangle area;
• Isosceles triangle side;
• Isosceles triangle height; and
• Triangle vertices.

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.

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!

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°.