Question

In ΔABC, if m ∠A = m∠C, m∠B = ß (where ß is an acute angle), and BC = x, which expression gives the length of b, the side opposite ∠B ?

Answer 1

Answer:

The length of b is $\sqrt{2x^2(1-cos\beta)}$.

Step by step explanation:

Given information: In ΔABC, ∠A =∠C, ∠B = ß (where ß is an acute angle), and BC = x.

Since two angles are same therefore triangle ABC is an isosceles triangle and side AB and BC are congruent.

$AB=BC=x$

According to Law of cosine

$b^2=a^2+c^2-2ac\cos B$

$b^2=x^2+x^2-2(x)(x)\cos \beta$

$b^2=2x^2-2x^2\cos \beta$

$b^2=2x^2(1-\cos \beta)$

$\sqrt{2x^2(1-cos\beta)}$

Therefore the length of b is $\sqrt{2x^2(1-cos\beta)}$.