Two ships are sailing in the sea on the two sides of a lighthouse. The angle of

CuriousTab

CuriousTab

Home Aptitude

Discussion

Home ‣ Aptitude ‣ Height and Distance Comments

Question
Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30� and 45� respectively. If the lighthouse is 100 m high, the distance between the two ships is:
Options
A. 173 m
B. 200 m
C. 273 m
D. 300 m

Correct Answer

273 m

Explanation
Let AB be the lighthouse and C and D be the positions of the ships.

Then, AB = 100 m, ∠ACB = 30� and ∠ADB = 45�.

AB	= tan 30� =	1	⟹ AC = AB x √3 = 100√3 m.
AC		√3

AB	= tan 45� = 1 ⟹ AD = AB = 100 m.
AD

∴ CD = (AC + AD)	= (100√3 + 100) m
	= 100(√3 + 1)
	= (100 x 2.73) m
	= 273 m.

Height and Distance problems

Search Results

1. The angle of elevation of the sun, when the length of the shadow of a tree √3 times the height of the tree, is:
Options
A. 30�
B. 45�
C. 60�
D. 90�

2. From a point P on a level ground, the angle of elevation of the top tower is 30�. If the tower is 100 m high, the distance of point P from the foot of the tower is:
Options
A. 149 m
B. 156 m
C. 173 m
D. 200 m

3. An observer 1.6 m tall is 20√3 away from a tower. The angle of elevation from his eye to the top of the tower is 30�. The heights of the tower is:
Options
A. 21.6 m
B. 23.2 m
C. 24.72 m
D. None of these

4. 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:
Options
A. 2.3 m
B. 4.6 m
C. 7.8 m
D. 9.2 m

5. A man standing at a point P is watching the top of a tower, which makes an angle of elevation of 30� with the man's eye. The man walks some distance towards the tower to watch its top and the angle of the elevation becomes 60�. What is the distance between the base of the tower and the point P?
Options
A. 4√3 units
B. 8 units
C. 12 units
D. Data inadequate
E. None of these

6. A sum of Rs. 12,500 amounts to Rs. 15,500 in 4 years at the rate of simple interest. What is the rate of interest?
Options
A. 3%
B. 4%
C. 5%
D. 6%
E. None of these

7. Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
Options
A. 3.6
B. 6
C. 18
D. Cannot be determined
E. None of these

8. How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
Options
A. 3.5 years
B. 4 years
C. 4.5 years
D. 5 years

9. A sum fetched a total simple interest of Rs. 4016.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?
Options
A. Rs. 4462.50
B. Rs. 8032.50
C. Rs. 8900
D. Rs. 8925
E. None of these

10. A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is:
Options
A. Rs. 650
B. Rs. 690
C. Rs. 698
D. Rs. 700

Comments

More in Aptitude: