Question

Consider an isoceles triangle with base a, vertical angle 20 and lateral side each being b

Answer 1

Consider any triangle ΔABC.ΔABC.

In right triangle ΔABD,ΔABD,

sinθ=BDABsin⁡θ=BDAB

BD=ABsinθBD=ABsin⁡θ

The area of this triangle is easy right?

ar(ΔABC)=12BD⋅ACar⁡(ΔABC)=12BD⋅AC

ar(ΔABC)=12AB⋅ACsinθar⁡(ΔABC)=12AB⋅ACsin⁡θ

We can generalise this as follows, the area of a triangle with consecutive sides a,ba,b and included angle θθ is 12absinθ.12absin⁡θ.

Apllying this to your question,

A=1220×20×12–√A=1220×20×12

A