# A Ladder on the Platform of a Fire Brigade Van Can Be Elevated at an Angle of 70° to the Maximum. the Length of the Ladder Can Be Extended Upto 20 M. If the Platform is 2m Above the Ground - Geometry

#### Question

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

#### Solution

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,
$\sin70^\circ = \frac{DE}{AD}$
$\Rightarrow 0 . 94 = \frac{h - 2}{20}$
$\Rightarrow h - 2 = 20 \times 0 . 94 = 18 . 8$
$\Rightarrow h = 18 . 8 + 2 = 20 . 8 m$

Thus, the maximum height from the ground upto which the ladder can reach is 20.8 m.

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