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.)

98 m

⇒ 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.)