Angle of Right Triangle Calculator

Created by Kenneth Alambra
Reviewed by Rahul Dhari
Last updated: Nov 28, 2022

This angle of a right triangle calculator will help you determine what the angles of a right triangle are - that is, if you know the measurements of at least two of its sides or at least one of its sides together with its area. Keep on reading to learn about:

  • How to find the angles of a right triangle;
  • How to use this calculator; and
  • Our other triangle calculators.

How to find the angles of a right triangle?

Since a triangle has a total of 180° for its internal angles, having one corner have an angle measurement of 90° means that the remaining two other angles should have a total of 90°. With that said, we can say that the two remaining angles α\alpha and β\beta are complementary angles. In equation form, we express that as:

α+β=90°\alpha + \beta = 90\degree

So, if we know one of these two angles, how to find the missing angles of a right triangle is as easy as subtracting our known angle from 90° 🙂.

On the other hand, if we do not know any of the two angles, we can still find them with the help of some basic trigonometric functions.

To find angle α\alpha, we can use the following equations:

  • α=arctan(a/b)\alpha = \arctan(a / b)
  • α=arccos(b/c)\alpha = \arccos(b / c)
  • α=arcsin(a/c)\alpha = \arcsin(a / c)

To determine angle β\beta, here are the equations we can use:

  • β=arctan(b/a)\beta = \arctan(b / a)
  • β=arccos(a/c)\beta = \arccos(a / c)
  • β=arcsin(b/c)\beta = \arcsin(b / c)

With those equations, we can see that if we have the measurements of at least two sides of our right triangle, we can determine what the angles of a right triangle are.

What if you only know the measurement of one leg? For that, you should at least also know the area of your right triangle to derive the other side of your triangle using one of these equations:

To find aa given the area\text{area} and bb:

a=2×area/ba = 2 \times \text{area} / b

To find bb given the \text{area} and aa:

b=2×area/ab = 2 \times \text{area} / a

Then you can use the formulas we previously discussed to find the missing angles of your right triangle.

The fun part is that we have already utilized these equations in this calculator for your convenience. Head to the next section of this text to learn how to use this tool for your angle of right triangle calculations 🙂.

🙋 Note that we cannot solve for the angles of a right triangle if we only know its hypotenuse cc and its area\text{area} because different right triangles can have the same hypotenuse but with different areas.

How to use our angle of right triangle calculator

To use our angle of a right triangle calculator, all you have to do is enter any two known sides of your right triangle. That could be the measurements of your right triangle's two legs (aa and bb), or one leg measurement and the hypotenuse (aa and cc, or bb and cc). You can also enter one of your triangle's sides (aa, bb, or cc) and the area\text{area} of your right triangle.

Upon doing so, you'll instantly see your right triangle's angles: both angle α\alpha and angle β\beta. It's that simple!

FAQ

What are the angles of a right triangle?

Let's say a right triangle has an area of 20 cm² and one of its legs equal to 4 cm. To find the angles of this right triangle:

  1. First, we find the other side of the triangle using this equation: b = 2 × area / a, where a = 4 cm. We'll then have b = 2 × 20 cm² / 4 cm =10 cm.
  2. Then we calculate the angle α opposite a to be equal to α = arctan(a / b): α = arctan(4 cm / 10 cm) =21.8°.
  3. Finally, we can subtract α from 90° to find β: β = 90° - 21.8° =68.2°.

What are the 3 angles of a right triangle?

The three angles of a right triangle are one 90° angle and two acute angles that are complementary angles. That means if a right triangle has one of its angles equal to 30°, its other angle would be 60°. On the other hand, if a right triangle is an isosceles triangle, its acute angles should both be 45° to meet this condition.

Kenneth Alambra
right triangle with sides a,b,c and angles α,β




a
in
b
in
c
in
Area
in²
Results
Angle α
deg
Angle β
deg
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