Class 10 Math: Some Applications of Trigonometry Important Exam Questions

NexPro Tools Mathematics TeamJune 5, 20266 min read

Preparing for school exams or final CBSE boards requires practicing questions patterned after official grading schemes. We have compiled a list of crucial questions for Class 10 Some Applications of Trigonometry to help you test your mastery.

Exam-Pattern Questions and Answers

Question 1 (HARD)

Aditya is a pilot in Air India. During the Covid -19 pandemic, many Indian passengers were stuck at Dubai Airport. The government of India sent special aircraft to take them. Mr. Vinod was leading this operation. He is flying from Dubai to New Delhi with these passengers. His airplane is approaching point A along a straight line and at a constant altitude h. At 10:00 am, the angle of elevation of the airplane is 30° and at 10:01 am, it is 60°. (i) What is the distance d is covered by the airplane from 10:00 am to 10:01 am if the speed of the airplane is constant and equal to 600 miles/hour? (ii) What is the altitude h of the airplane? (round

This is a descriptive problem. Work out all steps on paper before checking the solution.

Solution Explanation & Steps: wer to 2 decimal places) OR Find the distance between passenger and airplane when the angle of elevation is 60°. (iii) Find the distance between passenger and airplane when the angle of elevation is 30°. Ans: (i) Time covered 10.00 am to 10.01 am = 1 minute = 1/60 hour Given: Speed = 600 miles/hour Thus, distance d= 600 x (1/60) = 10 miles (ii) Now, 0 'tan 30 ' 10 BB h B A x= = + and 0 ' 'tan 60 ' ' CC BB h C A C A x= = = 0tan 60 3 h hx = = 0 3tan 30 10 310 3 h h h h \ = = ++ 1 3 3 10 3 2 10 3 3 10 3 h h h h h ⇒ = ⇒ = + ⇒ = + 5 3 8.66h miles⇒ = = Thus, the altitude 'h' of the airplane is 8.66 miles. OR (ii) The distance between passenger and airplane when the angle of elevation is 60°. In ∆ACC', 0 ' 3 5 3sin 60 10 2 CC AC milesAC AC= ⇒ = ⇒ = (iii) The distance between passenger and airplane when the angle of elevation is 30⁰. In ∆ABB', 0 ' 1 8.66sin 30 17.32 2 BB AB milesAB AB= ⇒ = ⇒ =

Question 2 (EASY)

A 1.6 m tall girl stands at distance of 3.2 m from a lamp post and casts shadow of 4.8 m on the ground, then the height of the lamp post is
  • Option 1: 8 m
  • Option 2: 4 m
  • Option 3: 6 m
  • Option 4: 8/3 m

Solution Explanation & Steps: (d) 8/3 m Let AB be the position of the give and PQ be the lamp post. Now, Δ OAB ∼ ΔOPQ (by AA similarity) 4.8 1.6 4.8 1.6 16 8 8 4.8 3.2 8 48 3 OA AB PQ mOP PQ PQ PQ ×\ = ⇒ = ⇒ = ⇒ = =+

Question 3 (HARD)

Case Study - 1 Ram is watching the top and bottom of a lighthouse from the top of the building. The angles of elevation and depression of the top and bottom of a lighthouse from the top of a 60 m high building are 30° and 60° respectively. Find (i) the difference between the heights of the lighthouse and the building. (ii) the distance between the lighthouse and the building. OR The ratio of the height of a light house and the length of its shadow on the ground is √3 : 1 What is the angle of elevation?

This is a descriptive problem. Work out all steps on paper before checking the solution.

Solution Explanation & Steps: In right ∆ABD, 0 60 60tan 60 3 20 3 3 AB BD mBD BD= ⇒ = ⇒ = = ∴ AE = 20√3 m (∵ BD = AE) Now in right ∆AEC 0 1tan 30 20 3 20 3 CE CE CE mAE= ⇒ = ⇒ = (i) Difference between the heights of the lighthouse and the building = CE = 20 m (ii) The distance between the lighthouse and the building = BD = 20√3 m. OR Let AB be the light house, BC be its shadow and θ be the angle of elevation of the sun at that instant Then, in triangle ABC, we have, tan θ = AB BC tan θ = 03 tan 601 = ⇒ θ = 60° Hence, angle of elevation of the sun is 60°.

Grading Step-Marking Guidelines

Remember that teachers award partial marks for writing down formulas, stating the given variables, and drawing diagrams. Never leave a question blank on an exam. Write down the relevant formulas and initial substitution steps to secure partial credits.

📚 Class 10 Math Resource Hub for Some Applications of Trigonometry: • 🧮 Interactive Solver: Solve Some Applications of Trigonometry Problems - Verify steps in real-time. • 📝 Timed Practice Quiz: Take Some Applications of Trigonometry Online Quiz - Test your speed and concepts. • 📄 Printable Worksheet: Download Some Applications of Trigonometry PDF Worksheet - Interactive problems with answers. • 📐 Formula Sheet: View Some Applications of Trigonometry Key Equations - Complete revision references. • 🔄 Next Topic Guide: Circles Study Notes • 🎓 Syllabus Overview: Class 10 Mathematics Portal - Access all chapter guides.