Trigonometry Part 3 Quiz

Trigonometry Part 3 Quiz makes learning angles of elevation and distances much more engaging. An interesting piece of trivia is that the ancient Greek mathematician Hipparchus is often called the father of trigonometry because he created one of the first known trigonometric tables. His work was designed to study the stars, yet the same principles are now applied to solving everyday problems. This blend of history and math shows how timeless the subject really is. By attempting this trigonometry word problems quiz, you will see how concepts of elevation and depression are not just theoretical but practical too. The quiz presents trigonometry MCQs with answers and helps you sharpen skills while solving heights and distances problems step by step.

Trigonometry Part 3

A kite is flying at a height of 60 m from level ground, attached to a string making an angle of elevation of 60°. Find the length of the string.

40/√3 m

60 m

40√3 m

40 m

A boy is standing 50 m from a tree. The angle of elevation to the top of the tree is 30°. Find the height of the tree.

50/√3 m

50√3 m

25 m

100

A tree casts a shadow 20 m long when the sun's angle of elevation is 30°. Find the height of the tree.

20√3

20/√3

From the top of a cliff 100 m high, the angle of depression of a boat is 30°. What is the distance of the boat from the base of the cliff?

100/√3

100√3

100/3

300

The angle of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line are complementary. Find the height of the tower.

The angle of elevation of the top of a building from a point on the ground is 30°. After walking 30 m towards the building, the angle of elevation becomes 60°.

15√3

15/√3

30√3

30/√3

A man observes the top of a building at an angle of elevation of 30°. If he moves 40 m closer, the angle becomes 60°. Find the height of the building.

20/√3

120

20√3

An observer 1.5 m tall is 28.5 m away from a chimney. The angle of elevation of the top of the chimney from his eye is 45°. What is the height of the chimney?

28.5

31.5

A statue 1.6 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the pedestal.

1.19

2.73

2.19

1.73

The angles of elevation of the top of a tower from points P and Q at distances of a and b respectively from the base and in the same straight line with it are complementary. What is the height AB?

√(ab)

√(a/b)

√(b/a)

a√b

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Sample Questions from This Quiz

A tree casts a shadow 20 m long when the sun’s angle of elevation is 30°. Find the height of the tree.
From the top of a cliff 100 m high, the angle of depression of a boat is 30°. What is the distance of the boat from the base of the cliff?
The angle of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line are complementary. Find the height of the tower.
The angle of elevation of the top of a building from a point on the ground is 30deg. After walking 30 m towards the building, the angle of elevation becomes 60°.
A man observes the top of a building at an angle of elevation of 30°. If he moves 40 m closer, the angle becomes 60°. Find the height of the building.

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