# Oblique Triangle Calculator

Even though triangles have only three sides and three angles, the data combinations are quite a lot: discover the many ways to solve an oblique triangle with our oblique triangle calculator.

## What is an oblique triangle?

An oblique triangle is any triangle without any particular constraint on the values of sides and angles, apart from the fundamental one: **an oblique triangle can't have a right angle**.

🙋 If you are looking for the mathematics of right triangles, head to our other calculators:

The definition of an oblique triangle includes all of the other types of triangles: obtuse, acute, equilateral, isosceles, and scalene.

There are no specific rules to solve an oblique triangle: we need to rely mostly on the two fundamental tools of the field:

- The
**law of sines**; and - The
**law of cosines**.

Let's see the possible ways we have to solve and calculate an oblique triangle!

## Solving an oblique triangle knowing three sides

This oblique triangle solver uses three sides to calculate a unique oblique triangle. Given $a$, $b$, and $c$, what do we do?

To calculate the perimeter and the area, we can skip every angle calculation. For the perimeter, we sum the given sides:

For the area, we can apply the **Heron's formula**:

Technically we can compute the angles of the triangle using the angle version of the **law of cosines**. Here is the formula for the third angle. You can derive the others on your own; they are fairly similar!

## Calculate an oblique triangle with two adjacent sides and the angle between them

This combination of data is usually denoted by the acronym **SAS**. You need to know the angle between the sides because it's the only one univocally defining a triangle. Other angles (as in the SSA combination) would allow for more than a possible shape. We will show you the calculations for the combination $a$, $b$, and $\gamma$.

We can calculate the area right away:

And apply the law of cosines to find the third side:

The other quantities follow: use the law of sines to find the other angles, or simply ask our oblique triangle calculator to do it for you!

## Calculations to solve an oblique triangle knowing two angles and a side

There are two possible ways to solve an oblique triangle knowing two sides and an angle:

**ASA**, where we know the two angles lying on a side (of which we know the length); or**AAS**, where we know two consecutive angles and one of the two sides not comprised between them.

#### ASA oblique triangle solver

Here we know any combination of two angles and the side between them, for example, $\beta$, $\gamma$, and $a$.

In this situation, firstly compute the value of the third angle:

Then apply the law of the sines to find the other two sides. Use the following equalities:

And derive:

Proceed to calculate the perimeter and the area with your preferred formulas!

#### AAS oblique triangle solver

Assume you know the angles $\beta$ and $\gamma$, and the side $b$.

Start by calculating the last angle:

Then, use again the law of the sines, but with regards to the other angle:

## How to use our oblique triangle calculator

To use our oblique triangle calculator, select the type of data you know: three sides, two sides and an angle, and so on. We will change the visible variables to fit the problem.

Fill the available fields, and find the results!

## Other triangle calculators

Here at Omni Calculator, we studied triangles from every possible side — wait, this doesn't sound so much. We made many tools related to this fundamental shape of geometry: discover triangles with our calculators:

- Triangle area calculator;
- AAA triangle calculator;
- Midsegment of a triangle calculator;
- Acute triangle calculator;
- Circumcenter of a triangle calculator;
- Triangle congruence calculator;
- Obtuse triangle calculator;
- Base of a triangle calculator;
- AAS triangle calculator;
- SAS triangle calculator;
- SSS triangle calculator; and
- ASA triangle calculator.

## FAQ

### What's the area of a triangle with sides a = 4 cm, b = 5 cm, and angle between them γ = 40°?

The area is `A = 6.428 cm²`

. This is an SAS triangle, which means that you provided two sides and the angle between them. We can apply the formula for the area of an SAS triangle:

`A = 0.5 × a × b × sin(γ) = 0.5 × 4 × 5 × 0.6428 = 6.428 cm²`

### Can you solve an SSA triangle?

No. An SSA triangle is not unambiguously defined by the given combination: in fact, you can find two triangles which respect the combination. Imagine the given side not adjacent to the given angle: it can be in two positions, one forming an acute angle with the other side, the other forming an obtuse angle.

### What are the possible combinations of sides and angles to solve an oblique triangle?

You can solve an oblique triangle if you know:

- Three sides (SSS triangle);
- Two sides and the angle between them (SAS triangle);
- Two angles and the side between them (ASA triangle); or
- Two angles and one of the two sides not lying between them (AAS triangle).

### How do I solve an AAS triangle?

To solve an AAS triangle, assuming you know `α`

, `β`

, and `b`

, follow these steps:

- Calculate the third angle using the sum of the interior angles in a triangle:
`γ = 180° - α - β`

. - Calculate the other sides using the law of sines:
`c = sin(γ) × b/sin(ß)`

`a = sin(α) × b/sin(ß)`

3 Calculate perimeter and area.

### How do I solve an ASA triangle?

To solve an ASA triangle, assuming you know `α`

, `β`

, and `c`

, follow these steps:

- Calculate the third angle using the sum of the interior angles in a triangle:
`γ = 180° - α - β`

. - Calculate the other sides using the law of sines:
`b = sin(ß) × c/sin(γ)`

`a = sin(α) × c/sin(γ)`

3 Calculate perimeter and area.