# Apex Angle of Isosceles Triangle Calculator - Calculate the Angle at the Apex of an Isosceles Triangle

 Base Angle °
 Apex Angle = °

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The Apex Angle of Isosceles Triangle Calculator is a useful tool for finding the angle at the apex of an isosceles triangle. In this tutorial, we'll show you how to use the calculator and provide you with some examples to help you understand how it works.

## Step 1: Enter the Length of the Base and the Length of One of the Equal Sides

The first step is to enter the length of the base and the length of one of the equal sides of the isosceles triangle into the input boxes on the calculator. Make sure to enter the values in the correct format and with the appropriate units.

## Step 2: Calculate the Half of the Base Length

Once you've entered the lengths, click the "Calculate Half of Base Length" button on the calculator. Our Apex Angle of Isosceles Triangle Calculator will then display the half of the base length.

b/2 = (b / 2)

As you can see from the formula above, the half of the base length is simply half of the length of the base of the isosceles triangle.

## Step 3: Calculate the Height of the Isosceles Triangle

Next, click the "Calculate Height" button on the calculator. Our Apex Angle of Isosceles Triangle Calculator will then display the height of the isosceles triangle.

h = √(a2 - (b/2)2)

As you can see from the formula above, the height of the isosceles triangle is calculated using the Pythagorean theorem.

## Step 4: Calculate the Apex Angle

Once you've calculated the height of the isosceles triangle, click the "Calculate Apex Angle" button on the calculator. Our Apex Angle of Isosceles Triangle Calculator will then display the angle at the apex of the isosceles triangle.

θ = 2 * arctan(h/b)

As you can see from the formula above, the angle at the apex of the isosceles triangle is calculated using the height of the isosceles triangle and half of the base length.

## Examples

Let's look at some examples to see how the Apex Angle of Isosceles Triangle Calculator works:

• An isosceles triangle with a base length of 6 units and an equal side length of 5 units has an apex angle of 57.79 degrees.
• An isosceles triangle with a base length of 10 units and an equal side length of 8 units has an apex angle of 35.54 degrees.
• An isosceles triangle with a base length of 12 units and an equal side length of 6 units has an apex angle of 63.43 degrees.

As you can see from these examples, our Apex Angle of Isosceles Triangle Calculator can calculate the angle at the apex of an isosceles triangle quickly and accurately.

## Conclusion

The Apex Angle of Isosceles Triangle Calculator is a valuable tool for finding the angle at the apex of an isosceles triangle. By following the simple steps outlined in this tutorial, you can quickly and accurately calculate the apex angle of an isosceles triangle using its base length and the length of one of its equal sides. Try it out for yourself and see how easy it is!

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