In ΔABC, right angled at C, if A = 8/7, then the value of cot B is (A) 7/8 (B) 8/7 (C) (7)/(√(113)) (D) (8)/(√(113))

MathsCBSE Class 10 · Basic · Board exam 2023, set 430/6/1 · 1 mark · MCQ

CBSE Class 10 Mathematics Basic 2023: question 3

Set in the CBSE Class 10 board exam of 2023, paper 430/6/1, section A, question 3, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q3 · 1 mark · MCQIntroduction to Trigonometry

In $Δ$ ABC, right angled at C, if $tan A = \frac{8}{7}$ , then the value of cot B is

(A) $\frac{7}{8}$
(B) $\frac{8}{7}$
(C) $\frac{7}{113}$
(D) $\frac{8}{113}$

Figure in the paper: Right triangle ABC with the right angle at C (marked with a square). Vertex B is at the top, A at the bottom left, C at the bottom right. The angle at A is marked. See it in the official paper.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2023 board paper, set 430/6/1.

Hints

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

Hint 1

In a triangle right-angled at C, $A + B = 9 0^{\circ}$ .

Hint 2

$cot (9 0^{\circ} - A) = tan A$ .

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.

$tan A = \frac{B C}{A C} = \frac{8}{7}$ .
$cot B = \frac{side adjacent to B}{side opposite to B} = \frac{B C}{A C} = \frac{8}{7}$ (equivalently $cot B = tan (9 0^{\circ} - B) = tan A$ ), so option (B).
1 mark

Answer: $\frac{8}{7}$ , option (B)

Where the marks are

Recognises $cot B = tan A = \frac{8}{7}$ (1 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 paper2023 board paper, set 430/6/1 (Basic): every question, by section.

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CBSE Class 10 Mathematics Basic 2023: question 3

Hints

Step-by-step solution

Revise the chapter

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