A. 173 m
B. 200 m
C. 273 m
D. 300 m
Let AB be the lighthouse and C and D be the
positions of the ships. Then,
AB = 100 m, ∠ACB = 300 and ∠ADB = 45°.
AB/AC = tan 30° = 1/√3
AC = AB X √3 = 100√3 m.
AB/AD = tan 45° = 1 ⇒ AD = AB = 100 m.
CD = (AC + AD) = (100√3 + 100) m
= 100 (√3 +1) m = (100 X 2.73) m = 273 m.
Related Mcqs:
- The top of a 15 metre high tower makes an angle of elevation of 60° with the bottom of an electric pole and angle of elevation of 30° with the top of the pole. What is the height of the electric pole ?
A. 5 metres
B. 8 metres
C. 10 metres
D. 12 metres - From a point P on a level ground, the angle of elevation of the top of a tower is 30°. If the tower is 100 m high, the distance of point P from the foot of the tower is :_________?
A. 149 m
B. 156 m
C. 173 m
D. 200 m - Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.
A. 225 cm2
B. 275 cm2
C. 285 cm2
D. 315 cm2 - The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is :_________?
A. 2.3 m
B. 4.6 m
C. 7.8 m
D. 9.2 m - A steamer goes downstream from one port to another in 4 hours, it covers the same distance upstream in 5 hours. If the speed of the stream is 2km/hr,the distance between the two parts is_______?
A. 50km
B. 60km
C. 70km
D. 80 km - A boats man can row in still water at speed of 7 km/hr. It takes 6 hours more to travel the same distance in upstream than in downstream if the speed of the river is 3 km/hr. what is the distance between the two destinations?
A. 20 km
B. 40 km
C. 30 km
D. 10 km - P and Q started a business investing Rs. 85,000 and Rs. 15,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively?
A. 3:4
B. 3:5
C. 15:23
D. 17:23
E. None of these - An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 5/3 hours, it must travel at a speed of:_________?
A. 660 km/hr
B. 680 km/hr
C. 700 km/hr
D. 720 km/hr - In two successive years, 100 and 75 students of a school appeared at the final examination. Respectively 75 % and 60 % of them passed. The average rate of pass is:_________?
A. 68 4/7 %
B. 78 %
C. 80 %
D. 80 4/7 % - If the height of a pole is 2√3 metres and the length of its shadow is 2 metres, find the angle of elevation of the sun.
A. 50°
B. 60°
C. 70°
D. 80°
