Question : A ladder leaning against a window of a house makes an angle of $60^{\circ}$ with the ground. If the distance of the foot of the ladder from the wall is 4.2 m, then the height of the point, where the ladder touches the window from the ground is closest to:
Option 1: 7.3 m
Option 2: 6.8 m
Option 3: 7.8 m
Option 4: 7 m
Correct Answer: 7.3 m
Solution :
Given, $BC = 4.2\ m$
In $\triangle ABC$
$AB$ is the height of the point, where the ladder touches the window from the ground.
$\tan 60^\circ = \frac{AB}{BC}$
⇒ $\sqrt 3 = \frac{AB}{4.2}$
⇒ $AB = 4.2 × 1.73 = 7.3$
Hence, the correct answer is 7.3 m.
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