Trigonometry Part 4 Quiz

Trigonometry Part 4 Quiz will put your skills to the test in a fun and exciting way. It’s a field of math that was crucial to the development of early navigation. Sailors would use trigonometric principles to determine their location at sea by measuring the angle of the stars above the horizon. This practical application of the trigonometry word problems quiz is a testament to its real-world importance. We have compiled a series of challenging questions that will sharpen your knowledge of heights and distances problems. Get ready to apply your knowledge and solve some intriguing puzzles in this test on trigonometry.

Trigonometry Part 4

An airplane is flying at an altitude of 1000 m. The angle of depression from the airplane to a point on the ground is 45°. What is the horizontal distance of the airplane from the point on the ground?

2000

1000√2

1000/√2

1000

A flagstaff stands on the top of a 50 m high building. The angle of elevation of the top of the flagstaff from a point on the ground is 60° and the angle of evation of the top of the building from the same point is 30°. Find the height of the flagstaff

50√3

150

100

A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank is 60°. When he moves 40 m away from the bank, the angle of elevation becomes 30°. What is the width of the river?

20√3

40√3

40/√3

A boy standing 30 m away from a tower observes the angle of elevation of the top of the tower as 30°. His eyes are 1.5 m above the ground. What is the height of the tower?

10√3 + 1.5

10√3

30√3 + 1.5

10√3 - 1.5

The angle of depression of two ships from the top of a lighthouse are 45° and 30° respectively. If the ships are on opposite sides of the lighthouse and the lighthouse is 100 m high, find the distance between the two ships.

100(√3 - 1)

100/(√3 - 1)

100(√3 + 1)

100

A straight tree breaks due to a storm. The broken part bends so that the top of the tree touches the ground at a distance of 8 m from the base. If the angle made by the broken part with the ground is 30°, find the original height of the tree.

8/√3

8(√3 - 1)

8√3

8(√3 - 1)

A person on a bridge observes a boat at an angle of depression of 30°. If the bridge is 25 m high, what is the distance of the boat from the bridge?

25√3

25/√3

50√3

50/√3

An aeroplane at an altitude of 1500 metres find that two ships are sailing towards it in the same direction. The angles of depression as observed from the aeroplane are 45° and 30° respectively. Find the distance between the two ships.

1500√3

1500/(√3 - 1)

1500(√3 + 1)

1500(√3 - 1)

If the length of a shadow cast by a pole be √3 times the length of the pole, find the angle of elevation of the sun.

60°

30°

45°

15°

The shadow of a vertical tower on a level ground increased by 10 m when the altitude of the sun changes from 45° and 30°. Find the height of the tower correct to two decimal place.

5/(√3 + 1)

5(√3 + 1)

5/(√3 - 1)

5(√3 - 1)

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Sample Questions from This Quiz

An airplane is flying at an altitude of 1000 m. The angle of depression from the airplane to a point on the ground is 45°. What is the horizontal distance of the airplane from the point on the ground?
A flagstaff stands on the top of a 50 m high building. The angle of elevation of the top of the flagstaff from a point on the ground is 60° and the angle of elevation of the top of the building from the same point is 30°. Find the height of the flagstaff
A person standing on the bank of a river observes that the angle of elevation of the top of a tree on the opposite bank is 60°. When he moves 40 m away from the bank, the angle of elevation becomes 30°. What is the width of the river?
A boy standing 30 m away from a tower observes the angle of elevation of the top of the tower as 30°. His eyes are 1.5 m above the ground. What is the height of the tower?
The angle of depression of two ships from the top of a lighthouse are 45° and 30° respectively. If the ships are on opposite sides of the lighthouse and the lighthouse is 100 m high, find the distance between the two ships.

Try the full quiz and see how many of these you can answer!