If in an isosceles triangle with base 'a', vertical angle `20^@` and lateral side each of length 'b' is given then value of `a^3+b^3` equals

Explanation

To solve the problem, we need to find the value of \( a^3 + b^3 \) for an isosceles triangle with a base \( a \), a vertical angle of \( 20^\circ \), and lateral sides of length \( b \).

### Step-by-Step Solution:

1. **Identify the Angles**:
In an isosceles triangle with a vertical angle of \( 20^\circ \), the other two angles (let's call them \( B \) and \( C \)) will each be:
\[
B = C = \frac{180^\circ - 20^\circ}{2} = 80^\circ
...