how find a side of triangle which two side equl and a angle is 120 degree

You have an isosceles triangle where two sides are equal and one angle is \( 120^\circ \). To find the length of the third side (let's call it \( c \)), you can apply the **Law of Cosines**.

### Given:
- Two equal sides \( a \) (so \( a = b \))
- The angle \( \angle C = 120^\circ \) between these two sides

### Formula:
The Law of Cosines states:

\[
c^2 = a^2 + b^2 - 2ab \cos(\angle C)
\]

Since \( a = b \) and \( \angle C = 120^\circ \):

\[
c^2 = a^2 + a^2 - 2a^2 \cos(120^\circ)
\]

Now, \( \cos(120^\circ) = -\frac{1}{2} \):

\[
c^2 = 2a^2 + a^2 =  3a squared end operation

Learn how to find the length of the third side of an isosceles triangle with two equal sides and an angle of 120 degrees using the Law of Cosines. This problem involves key geometric and trigonometric concepts, suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation