For acute angles A and B and A + 2B and 2A + B are acute if (A + 2B) = √(3) and (2A + B) = (1)/(√(2)), then find the measures of angles A and B.

MathsCBSE Class 10 · Standard · Board exam 2026, set 30/5/1 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard 2026: question 24(b)

Set in the CBSE Class 10 board exam of 2026, paper 30/5/1, section B, question 24(b), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q24(b) · 2 marks · Very short answerIntroduction to Trigonometry

For acute angles A and B and A + 2B and 2A + B are acute if $tan (A + 2 B) = 3$ and $sin (2 A + B) = \frac{1}{2}$ , then find the measures of angles A and B.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 30/5/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Which acute angle has tangent $3$ ? Which has sine $\frac{1}{2}$ ?

Hint 2

This gives two linear equations in A and B.

Hint 3

Add the two equations to find $A + B$ , then solve.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

$tan (A + 2 B) = 3 = tan 6 0^{\circ} \Rightarrow A + 2 B = 6 0^{\circ}$ ...(1)
½ mark
$sin (2 A + B) = \frac{1}{2} = sin 4 5^{\circ} \Rightarrow 2 A + B = 4 5^{\circ}$ ...(2)
½ mark
Adding (1) and (2): $3 A + 3 B = 10 5^{\circ} \Rightarrow A + B = 3 5^{\circ}$ ...(3). Subtracting (3) from (1): $B = 2 5^{\circ}$ .
½ mark
From (3): $A = 3 5^{\circ} - 2 5^{\circ} = 1 0^{\circ}$ .
½ mark

Answer: $A = 1 0^{\circ}$ , $B = 2 5^{\circ}$

Where the marks are

$A + 2 B = 6 0^{\circ}$ (½ mark)
$2 A + B = 4 5^{\circ}$ (½ mark)
$B = 2 5^{\circ}$ (½ mark)
$A = 1 0^{\circ}$ (½ mark)

Revise the chapter

Chapter: Introduction to Trigonometry (notes, formulas, where marks are lost and every past question)

Practise this chapterBoard-style questions from Introduction to Trigonometry, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 30/5/1 (Standard): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Standard 2026: question 24(b)

Hints

Step-by-step solution

Revise the chapter

More questions from Introduction to Trigonometry