# 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:

#### Example

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

#### 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.