From the top of a 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 $60^\circ$ and $45^\circ$, 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.)
Answer & explanation
Correct answer: option 1
⇒ AP = 36m
⇒ In triangle PAB
⇒ tan\({45}^\circ\) = \(\frac{PA}{AB}\)
⇒ 1 = \(\frac{36}{AB}\)
⇒ AB = 36 = PR
⇒ In triangle PQR,
⇒ tan\({60}^\circ\) = \(\frac{QR}{PR}\)
⇒ \(\sqrt {3 }\) = \(\frac{QR}{36}\)
⇒ QR = 36\(\sqrt {3 }\) = 61.2
⇒ QB = QR + RB (RB = PA)
⇒ QB = 61.2 + 36 = 97.2
⇒ QB = 98 (Approx.)