Some Applications of Trigonometry

Q1.From the top of a 75 m high lighthouse, the angles of depression of two ships are 30 degrees and 45 degrees. If the ships are on the same side, the distance between them is:

• A75(sqrt(3) - 1) m
• B75 sqrt(3) m
• C75 m
• D75(sqrt(3) + 1) m

Q2.A person observes the angle of elevation of a building as 30 degrees. On proceeding 40 m towards the building, the angle becomes 90 degrees. The height of the building is:

• A20/sqrt(3) m
• B20 m
• C40/sqrt(3) m
• D40 m

Q3.From the top of a 7 m high building, the angle of elevation of the top of a cable tower is 60 degrees and the angle of depression of its foot is 45 degrees. The height of the tower is:

• A7(sqrt(3) + 1) m
• B14 sqrt(3) m
• C7 sqrt(3) m
• D7(sqrt(3) - 1) m

Q4.A person standing at the bank of a river finds that the angle of elevation of the top of a tower on the other bank is 45 degrees. On retreating 50 m, the angle becomes 30 degrees. The width of the river is:

• A25(sqrt(3) + 1) m
• B50/(sqrt(3) - 1) m
• C25 sqrt(3) m
• DBoth a and b

Q5.A person standing on a hill observes two consecutive kilometre stones on a road at angles of depression 30 degrees and 60 degrees. The height of the hill is:

• Asqrt(3)/2 km
• B500 sqrt(3) m
• C1000 sqrt(3)/2 m
• DAll of the above