Worksheets › Class 10 › Some Applications of Trigonometry
Class 10 Some Applications of Trigonometry worksheet
CBSE Mathematics. Heights and distances with angles of elevation and depression. Every sheet has 20 questions in three sections and an answer key, and the numbers change every time.
Sample questions
Real questions from this chapter, as the app sets them. Tap Answer to see the answer and working.
Section A · multiple choice
- 1.
From a point on the ground 15 m from the foot of a clock tower, the angle of elevation of its top is 45°. Its height is:
- 15 m
- 30 m
- 15√3 m
- 5√3 m
Answer
(a) 15 m
height = 15 × tan 45° = 15 m
- 2.
The angle of elevation of the top of a lighthouse 60 m high, from a point on level ground, is 60°. How far is the point from its foot?
- 60√3 m
- 60 m
- 20√3 m
- 120 m
Answer
(c) 20√3 m
distance = 60 ÷ tan 60° = 20√3 m
- 3.
A kite is flying at a height of 63 m. Its string makes an angle of 30° with the ground. Taking the string as straight, its length is:
- 42√3 m
- 63 m
- 63√2 m
- 126 m
Answer
(d) 126 m
length = 63 ÷ sin 30° = 126 m
Section B · short answer
- 4.
A tree breaks in a storm. The broken part bends so that its top touches the ground 2 m from the foot of the tree, making an angle of 60° with the ground. Find the height of the tree before it broke.
Answer
(4 + 2√3) m
standing part = 2 tan 60° = 2√3; broken part = 2/cos 60° = 4; total = 4 + 2√3
- 5.
The angles of elevation of the top of a tower from two points on the ground, on the same side and in line with its foot, are 30° and 60°. The points are 26 m apart. Find the height of the tower.
Answer
13√3 m (the nearer point is 13 m from the foot)
h = x√3 and h = (x + 26)/√3, so 3x = x + 26, x = 13, h = 13√3
Section C · long answer
- 6.
An aeroplane flies horizontally at a height of 1,620 m. From a point on the ground, the angle of elevation of the plane changes from 60° to 30° in 30 seconds. Find its speed.
Answer
36√3 m/s
horizontal distances 1620/√3 and 1620√3; it flies 1620√3 − 1620/√3 = 1080√3 m in 30 s
Fresh sheets for your child
In the app, every Some Applications of Trigonometry sheet is new: the app remembers the questions your child has already had and leaves them out. Print the sheet as a PDF, or use notebook mode and write the answers in a notebook.
Coming soon for Android and iPhone.