Trig Triangle Calculator

If you're dealing with trigonometry and right triangles, this trig calculator for right triangles is here for you. This tool uses trigonometry to calculate these triangles, as long as you know:

• Two of its sides;
• One angle and one side; or
• The area and one side.

To learn more, keep reading this article that briefly discusses the trigonometry behind right triangles.

This trig triangle calculator uses the following widely-known trigonometric ratios, which relate the sides of a right triangle to its angles:

Additionally, we can use the inverse trigonometric functions to solve for the angles if we know the length of the sides:

Let's use the following triangle to explain how this calculator solves for the different sides and angles according to the information known.

Finding the third side

If you know two sides, the easiest way to find the third side is by using the Pythagorean theorem (what is the Pythagorean theorem).

• Given a and b: $c = \sqrt{a^2 + b^2}$;
• Given a and c: $b = \sqrt{c^2 - a^2}$; and
• Given b and c: $a = \sqrt{c^2 - b^2}$.

Finding the angles

Then, we can find $\alpha$ or $\beta$ by taking any of the inverse trigonometric functions mentioned previously:

Finding the angle

The sum of the internal angles of a triangle will always be $360\degree$. In a right triangle, there's a right angle ($90\degree$) and, therefore, the sum of the other two angles ($\alpha$ and $\beta$) will be $90\degree$. Therefore:

• Given $\beta$: $\alpha = 90\degree - \beta$; or
• Given $\alpha$: $\beta = 90\degree - \alpha$

Finding the two missing sides

To find the two unknown sides, you can use the angle $\alpha$ and the trigonometric ratios:

• Given a: $c = a/{\sin{\alpha}}$ and $b = a/{\tan{\alpha}}$;

• Given b: $c = b/{\cos{\alpha}}$ and $a = b \times {\tan{\alpha}}$; and

• Given c: $a = c \times \sin{\alpha}$ and $b = c \times {\cos{\alpha}}$;

If you know $a$ or $b$, use the right triangle area formula that relates the base ($b$) to the height ($a$) and solve for the unknown side:

• Given a: $b = 2 \times \text{Area}/a$; and
• Given b: $a = 2 \times \text{Area}/b$.

Once you know at least two sides, use the second section method to obtain the angles.

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