Class 10 Math: Some Applications of Trigonometry Important Exam Questions
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)
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)
- 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)
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.