Question

In a triangle ABC the altitudes from B and C on to the opposite sides are not shorter than their respective opposite sides. Then one of the angles of ABC is

• A. ${30}^o$
• B. ${45}^o$
• C. ${60}^o$
• D. ${72}^o$

Answer 1

The correct option is B ${45}^o$

BD $\ge$ b and CE $\ge$ c
c sin A $\ge$ b ............ (i)
and b sin A $\ge$ c ............ (ii)
(i) + (ii)
(c + b) sin A $\ge$ b + c
sin A $\ge$ 1
$\therefore A={90}^o$
Now from (i) and (ii)
$c\ge b$ and $b\ge c$
$c=b$ Hence angles are ${45}^o,{45}^o,{90}^o$