Question

In ΔABC, ∠ACB > 90°. The correct relation is ______.

Options

• AB² > BC² + AC²

• BC² > AC² + AB²

• AC² > AB² + BC²

• AB² = BC² + AC²

Answer 1

In ΔABC, ∠ACB > 90°. The correct relation is AB² > BC² + AC².

Explanation:

∠ACB is obtuse > 90°.

So, the side opposite it (AB) is longest. 

By the law of cosines,

AB² = AC² + BC² – 2·AC·BC·cos(∠ACB). 

Since cos (∠ACB) < 0, the term –2·AC·BC·cos(∠ACB) is positive.

So, AB² > AC² + BC².