Some Applications of Trigonometry Assertion–Reason PYQs Class 10 CBSE (With Answers)

Practise one selected Some Applications of Trigonometry Assertion–Reason question from CBSE Class 10 previous-year board papers. Check each statement, then decide whether the Reason explains the Assertion. Two true statements do not always form a correct explanation.

1 distinct question · 3 board-paper appearances
Solutions prepared by Team TutorVertex · Reviewed: 25 October 2026

LevelSourceTopic

Showing 1 of 1 questions.

Ladders, heights and distances

Key results

In a right triangle, hypotenuse² = vertical side² + horizontal side².
For the angle θ with the horizontal, tan θ = $\frac{vertical height difference}{horizontal distance}$ .
A ladder is the hypotenuse; its length is different from the height it reaches on the wall.

Question 1 · Standard

Assertion (A): A ladder leaning against a wall, stands at a horizontal distance of 6 m from the wall. If the height of the wall up to which the ladder reaches is 8 m, then the length of the ladder is 10 m.

Reason (R): The ladder makes an angle of 60° with the ground.

Appeared in: 2025 · Standard

A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).B. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).C. Assertion (A) is true but Reason (R) is false.D. Assertion (A) is false but Reason (R) is true.

Show Answer & Explanation

Official CBSE answer · Explanation by Team TutorVertex

Assertion: True.
Let AB be the vertical height reached, BC the horizontal distance from the wall, and AC the ladder.
Here AB = 8 m, BC = 6 m and ∠ABC = 90°.
By Pythagoras’ theorem, AC² = AB² + BC²
= 8² + 6²
= 100.
Therefore AC = 10 m.

Reason: False.
Let θ = ∠ACB, the angle between the ladder and the ground.
Then tan θ = $\frac{AB}{BC}$ = $\frac{8}{6}$ = $\frac{4}{3}$ .
But tan 60° = √3.
Since $\frac{4}{3}$ ≠ √3, the ladder does not make an angle of 60° with the ground.

Link: A is true by Pythagoras’ theorem. R gives an incorrect angle, so R is false. Answer: C.

Solution diagram by TutorVertex. AB is the wall height, BC the horizontal distance and AC the ladder.

Common questions

Is the ladder length the same as the height reached?

No. The ladder is the hypotenuse. The height reached is the vertical side of the right triangle.

How can I check whether the angle is 60°?

Calculate vertical height divided by horizontal distance. This equals tan θ. Compare it with tan 60° = √3.

Do I need to find the angle in decimal degrees?

No. To test a claimed standard angle, compare the calculated ratio with its exact trigonometric value.

When should I include the observer’s height?

When the line of sight starts above ground level, the right triangle uses the difference between the object’s height and the observer’s eye level. Add the eye-level height back when finding the object’s total height.

Official sources and marking schemes

Source labels identify the original paper, set and question number. ZIP links open official archives containing the named paper.

Question source details

Question 1 sources

The Assertion, Reason and A–D choice meanings and order match across all three listed papers. Punctuation is standardised.

Board papers

2025 board papers

NCERT and syllabus

About these solutions

The displayed answer keys have been matched to official CBSE marking schemes. Explanations are written by Team TutorVertex using NCERT-style methods. Repeated questions are merged; all verified appearances and the original paper details are listed in the sources.

Answer key

Answer to the question above.
Question	Correct choice
Q1	C

Understand the reason behind the answer.

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How to solve Assertion–Reason questions

In the official 2026–27 sample papers, Q19 and Q20 in Section A are Assertion–Reason questions worth one mark each. Basic format · Standard format.

Check whether the Assertion is true.
Check whether the Reason is true, separately.
If both are true, decide whether the Reason explains the Assertion.
Match your conclusion to the printed answer choices.

Decision table for the standard choices used on this page
A true?	R true?	R explains A?	Choose
Yes	Yes	Yes	A
Yes	Yes	No	B
Yes	No	—	C
No	Yes	—	D