February 21, 2021

Chapters

- 1. Solve a Triangle Knowing: One Side and Two Adjacent Angles.
- Example
- 2. Solve a Triangle Knowing Two Sides and an Included Angle.
- Example
- 3. Solve a Triangle Knowing Two Sides and the Opposite Angle.
- 1. sin B > 1. No solution
- 2. sin B = 1. One Solution: Right Triangle
- 3. sin B < 1. One or Two Solutions
- 4. Solve a Triangle Knowing Two Sides and the Opposite Angle.

**Triangle** is a shape in the world of geometry. The word triangle can be broken into two parts. The first part is the **tri **and it means **three **and the second part is the **angle. **Hence, the meaning of triangle is a geometry of **three lines** which are making **three angles**. However, there are a few types of a triangle that differentiate from other triangles. The variation you will find will be in angles and lengths. Below are the types of triangles:

- Equilateral Triangle
- Isosceles Triangle
- Oblique Triangle

An **oblique triangle** does not have a right angle and can also be classified as an **acute triangle** or an **obtuse triangle**. The specialty of an oblique triangle is that it has all different angles and different lengths.

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: and .

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

## Example

Solve the oblique triangle with the following data: and °.

because and that is why, obtuse angle is A.

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

, If:

will result in **no solution**.

will result in **one solution**.

will result in **one or two solutions**.

## 1. sin B > 1. No solution

Solve the triangle with the following data: and .

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: , and .

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

Solve the triangle with the following data: , and .

As there is one solution which is

Solve the triangle with the following data: , and .

As therefore, there are two solutions:

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

Solve the triangle with the following data: , and .