# Oblique Triangles

An **oblique triangle** does not have a right angle and can also be classified as an **acute triangle** or an **obtuse triangle**.

To solve **oblique triangles**, use the **laws of sine and cosine**. There are **four different potential scenarios**:

#### 1. Solve a Triangle Knowing: One Side and Two Adjacent Angles.

#### Example

Solve the oblique triangle with the following data: a = 6 m, B = 45° and C = 105°.

#### 2. Solve a Triangle Knowing Two Sides and an Included Angle.

#### Example

Solve the oblique triangle with the following data: a = 10 m, b = 7 m and C = 30°.

#### 3. Solve a Triangle Knowing Two Sides and the Opposite Angle.

sin B > 1. No solution

sin B = 1. One solution

sin B < 1. One or two solutions

#### 1. sin B > 1. No solution

Solve the triangle with the following data: A = 30°, a = 3 m and b = 8 m.

Since the sine of an angle can never be greater than 1, the problem has no solution. The drawing above shows the impossibility of the situation.

#### 2. sin B = 1. One Solution: Right Triangle

Solve the triangle with the following data: A = 30°, a = 3 m and b = 6 m.

#### 3. sin B < 1. One or Two Solutions

Solve the triangle with the following data: A = 60°, a = 8 m and b = 4 m.

Solve the triangle with the following data: A = 30°, a = 3 m and b = 4 m.

#### 4. Solve a Triangle Knowing Two Sides and the Opposite Angle.

Solve the triangle with the following data: a = 15 m, b = 22 m and c = 17 m.