Mathematics: 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 ?

The answer is B) Similar to cash...

In δabc, if m ∠a = m∠c, m∠b = ß (where ß is an acute

Nico8776

06.01.2022

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

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