A ladder set against a wall at an angle 45° to the ground. If the foot of the ladder is pulled away from the wall…
CBSE Class 10 Maths PYQ · Applications of Trig · Double Triangle · 5 Marks · March 2023 · Standard
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365 Marks · March 2023 · Standard
A ladder set against a wall at an angle $45^{\circ}$ to the ground. If the foot of the ladder is pulled away from the wall through a distance of 4 m, its top slides a distance of 3 m down the wall making an angle $30^{\circ}$ with the ground. Find the final height of the top of the ladder from the ground and length of the ladder.
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1 for correct figure $\sin 45^{\circ} = \frac{AB}{BD} = \frac{h+3}{BD}$ $\Rightarrow BD = (h + 3) \sqrt{2}$ ----- (i) $\sin 30^{\circ} = \frac{h}{CE} = \frac{1}{2}$ $\Rightarrow CE = 2h$ ----- (ii) length of ladder remains same Therefore $BD = CE \Rightarrow (h + 3) \sqrt{2} = 2h$ $\Rightarrow h = \frac{3\sqrt{2}}{2-\sqrt{2}} = 3(\sqrt{2} + 1)$ Final height of the top of the ladder = $3(\sqrt{2} + 1) \text{ m}$ and length of ladder = $2h = 6(\sqrt{2} + 1) \text{ m}$
