Trigonometry and Its Applications (Class 10)

What this worksheet covers

This is an eighteen-question practice worksheet on trigonometry and its applications for Class 10, written to the pattern of the SOF International Mathematics Olympiad (IMO). It carries 24 marks and is designed to be attempted in 45 minutes, split across three sections — Mathematical Reasoning, Everyday Mathematics and Reasoning and Achievers Section. Every question is multiple choice with exactly one correct option, and every one comes with a fully worked solution rather than just an answer key — so a child who gets one wrong can see where the reasoning went astray instead of only learning that it did.

Skills your child practises

• Applied problem-solving on trigonometry and its applications at Class 10 level
• Working accurately against a time limit, as the real paper demands
• Mathematical Reasoning questions in the olympiad format
• Everyday Mathematics and Reasoning questions in the olympiad format
• Achievers Section questions in the olympiad format
• Reading worked solutions to find the step that went wrong

How to use it

1. 1There are 18 questions in this worksheet. All questions are compulsory.
2. 2Each question has four options (A), (B), (C) and (D). Exactly one option is correct.
3. 3Questions 1–15 carry 1 mark each. Questions 16–18 (Achievers Section) carry 3 marks each.
4. 4There is no negative marking. Use of a calculator is not allowed.
5. 5Figures are not drawn to scale unless stated. Rough work may be done at the side of each page.

Sample questions from this worksheet

A preview of what's inside Trigonometry and Its Applications (Class 10) — the PDF has the full set, and every question comes with a worked solution like these.

1. 1. In a right-angled triangle, sin θ is defined as _______.

   • A{opposite side/hypotenuse}correct
   • B{adjacent side/hypotenuse}
   • C{opposite side/adjacent side}
   • D{hypotenuse/opposite side}
   Solution: By definition sin θ = {opposite side/hypotenuse}. The adjacent side over the hypotenuse gives cos θ, and the opposite over the adjacent gives tan θ.

2. 2. If sin θ = {3/5}, then cos θ equals _______.

   • A{3/4}
   • B{5/4}
   • C{4/5}correct
   • D{5/3}
   Solution: Using sin²θ + cos²θ = 1, cos²θ = 1 − {9/25} = {16/25}, so cos θ = {4/5} for an acute angle. The triangle is the familiar 3–4–5 one.

3. 3. The angle of elevation of the top of a tower from a point on the ground is 30°. On walking 20 m towards the tower, the elevation becomes 60°. The height of the tower is _______.

   • A10√3 mcorrect
   • B10 m
   • C20√3 m
   • D20 m
   Solution: Let the height be h. From the far point the distance is {h/tan 30°} = h√3, and from the near point it is {h/tan 60°} = {h/√3}. The difference is the 20 m walked: h√3 − {h/√3} = 20, that is {3h − h/√3} = 20, so {2h/√3} = 20 and h = 10√3 m ≈ 17.3 m.