Properties Of Triangles — Important Questions

13

Using $a^2 = b^2 + c^2 - 2bc \cos A$, we get $a^2 = 9 + 16 - 2(3)(4)(0.5) = 25 - 12 = 13$.

Heron’s formula

Heron’s formula $\Delta = \sqrt{s(s-a)(s-b)(s-c)}$ is used when all three sides are known and $s = \frac{a+b+c}{2}$.

∠A = ∠B

If two sides of a triangle are equal, then the angles opposite to them are also equal. So $a = b \Rightarrow \angle A = \angle B$.

√[(s−b)(s−c)/bc]

The half-angle formula for sine is $\sin \frac{A}{2} = \sqrt{\frac{(s-b)(s-c)}{bc}}$.