Question

From the adjoining figure, find:

1. The longest side of ΔABC
2. The nature of ∠ВАС.

Answer 1

Given: The figure shows AD ⟂ BC with ∠ABC = 40° at B and ∠ACB = 26° at C (see the adjoining figure).

Step-wise calculation:

1. Sum of angles in ΔABC:

∠BAC + ∠ABC + ∠ACB = 180°

2. So, ∠BAC

= 180° – 40° – 26°

= 114°

3. The largest angle of a triangle lies opposite the longest side.

Here, the largest angle is ∠BAC = 114°.

So, the side opposite it is BC.

4. Since ∠BAC = 114° > 90°, ∠BAC is an obtuse angle.

 i. Longest side of ΔABC is BC.

ii. ∠BAC = 114°, so ∠BAC is obtuse.