Question

A ladder on the platform of a fire brigade van can be elevated at an angle of ${70}^{\circ }$to the maximum. The length of the ladder can be extended upto $20m$. If the platform is 2m above the ground, find the maximum height from the ground upto which the ladder can reach.$(\sin {70}^{\circ }=0.94)$

• A. $20.2m$
• B. $18.2m$
• C. $20.8m$
• D. $18.8m$

Answer 1

The correct option is C $20.8m$

Let AB be the platform of the fire brigade van and AD be the ladder.

Suppose the maximum height from the ground upto which the ladder can reach be h m.
Here, AB = 2 m, AD = 20 m, ∠DAE = 70º and AE ⊥ CD.

DE = CD − CE = (h − 2) m (CE = AB)

In right ∆AED,
$\sin {70}^{\circ }=\frac{DE}{AD}$
Thus, the maximum height from the ground upto which the ladder can reach is 20.8 m.
$\Rightarrow 0.94=\frac{h-2}{20}$
$\Rightarrow h-2=20\times 0.94=18.8$
$\Rightarrow h=18.8+2=20.8m$