Maths · Trigonometry · chapter 9 of 14
Class 10 Maths Chapter 9: Some Applications of Trigonometry case study question with answers
One case-based question of the kind the board asks in Section E: a passage and a table, then 3 parts worth 4 marks in all, with the answer and the marking scheme for each. Written from the NCERT chapter.
Case study · 4 marks
For a mathematics project, three students of a school in Nagpur measure the height of the school's clock tower with a home-made clinometer. Each holds the clinometer at eye level, measures the horizontal distance from the foot of the tower with a tape, and reads the angle of elevation of the top. All three have eyes 1.4 m above the level ground. Their readings are in the table.
| Student | Eye height | Distance from foot | Angle of elevation |
|---|---|---|---|
| Riya | 1.4 m | 24 m | 45° |
| Kabir | 1.4 m | 8√3 m | 60° |
| Meera | 1.4 m | 24√3 m | ? |
Part 1 · 1 mark
From Riya's reading, the height of the top of the tower above her eye level is
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Answer: (b) 24 m
tan 45° = h/24 and tan 45° = 1, so h = 24 m above eye level.
Part 2 · 1 mark
The height of the clock tower is
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Answer: (c) 25.4 m
Add back the eye height: 24 + 1.4 = 25.4 m.
Part 3 · 2 marks
Show that Kabir's reading gives the same height of the tower as Riya's.
Answer and marking scheme
Above Kabir's eye: 8√3 tan 60° = 8√3 × √3 = 24 m. Adding 1.4 m gives 25.4 m, the same as from Riya's reading.
- 8√3 tan 60° = 24 m (1)
- adds 1.4 m: 25.4 m, same height (1)
Or
Find the angle of elevation Meera should read.
Answer and marking scheme
Above her eye the top is 25.4 − 1.4 = 24 m. tan θ = 24/(24√3) = 1/√3, so θ = 30°.
- vertical side = 24 m, tan θ = 24/(24√3) (1)
- tan θ = 1/√3, θ = 30° (1)
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