Question

In ∆АВC, ∠A = 68°, AB = AC. Find the longest side of ∆AВС.

Answer 1

Given: In triangle ABC, ∠A = 68° and AB = AC isosceles with vertex A.

Step-wise calculation:

1. AB = AC

⇒ Angles opposite them are equal.

So, ∠B = ∠C.

2. Sum of angles: ∠A + ∠B + ∠C = 180°.

Substitute: 68° + 2∠B = 180°.

3. Solve:

2∠B = 180° – 68°

= 112°

⇒ ∠B = 56°

Thus, ∠C = 56°.

4. The largest angle in the triangle is ∠A = 68° and the longest side is the side opposite the largest angle.

The longest side of triangle ABC is BC.