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.
