Question : A ladder is resting against a wall, The angle between the foot of the ladder and the wall is 45o and the foot of the ladder is 6.6 m away from the wall. The length of the ladder (in m) is:
Option 1: $6.6 \times\sqrt{2}$
Option 2: $3.3 \times \sqrt{2}$
Option 3: $2.2 \times \sqrt{2}$
Option 4: $3.6 \times \sqrt{2}$
Correct Answer: $6.6 \times\sqrt{2}$
Solution :
Let the length of the ladder as $L$.
$\cos\theta = \frac{\text{Base}}{\text{Hypotenuse}}$
Since $\theta$ = 45º
So, cos 45º = $\frac{6.6}{L}$
⇒ $\frac{1}{\sqrt{2}}$ = $\frac{6.6}{L}$
⇒ $L = \frac{6.6}{\frac{1}{\sqrt{2}}}$
⇒ $L = {6.6}\times{\sqrt{2}}$
Hence, the correct answer is ${6.6}\times{\sqrt{2}}$.
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