A poster is on top of a building. Rajesh is standing on the ground at a distance of 50 m from the building. The angles of elevation to the top of the poster and bottom of the poster are 45° and 30° respectively. What is the height of the poster?
A. $$\frac{{50}}{{\sqrt 3 }}\left( {\sqrt 3 - 1} \right)$$
B. $$50\sqrt 3 \,{\text{m}}$$
C. $$50\sqrt 3 \,{\text{m}}$$
D. None of these
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & {\text{in}}\,\Delta PNQ,\,\tan {45^ \circ } = \frac{{PQ}}{{NQ}} \cr & \therefore PQ = NQ = 50{\text{m}} \cr & {\text{in}}\,\Delta MNQ,\,\tan {30^ \circ } = \frac{{MQ}}{{NQ}} \cr & \therefore \frac{1}{{\sqrt 3 }} = \frac{{MQ}}{{50}} \cr & \therefore MQ = \frac{{50}}{{\sqrt 3 }} \cr & \therefore h = PM \cr & \,\,\,\,\,\,\,\,\,\, = PQ - MQ \cr & \,\,\,\,\,\,\,\,\,\, = 50 - \frac{{50}}{{\sqrt 3 }} \cr & \,\,\,\,\,\,\,\,\,\, = \frac{{50}}{{\sqrt 3 }}\left( {\sqrt 3 - 1} \right) \cr} $$
∴ Poster height = $$\frac{{50}}{{\sqrt 3 }}\left( {\sqrt 3 - 1} \right)$$
Related Questions on Height and Distance
A. 173 m
B. 200 m
C. 273 m
D. 300 m
E. None of these
A. 4 √3 units
B. 8 units
C. 12 units
D. Data inadequate
E. None of these
A. 21.6 m
B. 23.2 m
C. 24.72 m
D. None of these
Join The Discussion