Question : From the top of house A in a street, the angles of elevation and depression of the top and foot of another house B on the opposite side of the street are 60° and 45°, respectively. If the height of house A is 36 m, then what is the height of house B? (Your answer should be nearest to an integer.)
Option 1: 91 m
Option 2: 98 m
Option 3: 94 m
Option 4: 93 m
Correct Answer: 98 m
Solution :
Given, AP = 36m
In $\triangle PAB$,
$⇒ \tan45^\circ = \frac{PA}{AB}$
$⇒ 1 = \frac{36}{AB}$
$⇒ AB = 36$ m
$⇒ AB = PR = 36$ m
In $\triangle PQR$,
$⇒ \tan60^\circ = \frac{QR}{PR}$
$⇒ \sqrt3 = \frac{QR}{36}$
$⇒ QR = 36 \sqrt3 = 36 × 1.732 = 62.35$
Now, $QB = QR + RB$
$⇒ QB = 62.35 + 36 = 98.35$
$⇒ QB \approx 98$ m
Hence, the correct answer is 98 m.
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