Question 2 - Case Based Questions (MCQ) - Chapter 8 Class 10 Introduction to Trignometry (Term 1)

Last updated at Aug. 18, 2021 by Teachoo

Authority wants to construct a slide in a city park for children. The slide was to be constructed for children below the age of 12 years. Authority prefers the top of the slide at a height of 4 m above the ground and inclined at an angle of 30° to the ground. Based on the following figure related to the slide answer the questions:

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Question 1

The distance of AB is:

(a) 8 m (b) 6 m

(c) 5 m (d) 10 m

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Question 2

The value of sin
^{
2
}
30° + cos
^{
2
}
60° is:

(a) 1/4 (b) 1/2

(c) 3/4 (d) 3/2

Question 3

If cos A = 1/2 , then the value of 12 cot
^{
2
}
A – 2 is:

(a) 5 (b) 4

(c) 3 (d) 2

Question 4

In the given figure, the value of (sin C × cos A) is:

(a) 1/3 (b) 1/2

(c) 1/4 (d) 1/5

Question 5

In the given figure, if AB + BC = 25 cm and AC = 5 cm, then the value of BC is:

Question Authority wants to construct a slide in a city park for children. The slide was to be constructed for children below the age of 12 years. Authority prefers the top of the slide at a height of 4 m above the ground and inclined at an angle of 30° to the ground. Based on the following figure related to the slide answer the questions: Question 1 The distance of AB is: (a) 8 m (b) 6 m (c) 5 m (d) 10 m In Δ ABC
sin 30° = 𝐴𝐶/𝐴𝐵
1/2 = 4/𝐴𝐵
AB = 8 m
So, the correct answer is (A)
Question 2 The value of sin2 30° + cos2 60° is: (a) 1/4 (b) 1/2 (c) 3/4 (d) 3/2 Now,
sin2 30° + cos2 60° = (1/2)^2+(1/2)^2
= 1/4 + 1/4
= 2/4
= 𝟏/𝟐
So, the correct answer is (B)
Question 3 If cos A = 1/2 , then the value of 12 cot2 A – 2 is: (a) 5 (b) 4 (c) 3 (d) 2 Given,
cos A = 1/2
cos A = cos 60°
∴ A = 60°
Now,
12cot2 A − 2 = 12 (cot 60°) − 2
= 12 (1/√3)^2−2
= 12 × 1/3 − 2
= 4 − 2
= 2
So, the correct answer is (D)
Question 4 In the given figure, the value of (sin C × cos A) is: (a) 1/3 (b) 1/2 (c) 1/4 (d) 1/5 Since AC ⊥ BC
∴ ∠ C = 90°
And,
∠ B = 30°
Now,
Sum of angles in Δ ABC = 180°
∠ A + ∠ B + ∠ C = 180°
∠ A + 90° + 30° = 180°
∠ A + 120° = 180°
∠ A = 180° − 90° − 30°
∠ A = 180° − 120°
∠ A = 60°
Thus,
sin C × cos A = sin 90° × cos 60°
= 1 × 1/2
= 𝟏/𝟐
So, the correct answer is (B)
Question 5 In the given figure, if AB + BC = 25 cm and AC = 5 cm, then the value of BC is: (a) 25 cm (b) 15 cm (c) 10 cm (d) 12 cm Let BC = x cm
Since AB + BC = x
AB + x = 25
AB = 25 − x
Now, In right triangle Δ ABC
By using Pythagoras theorem,
AB2 = BC2 + AC2
(25 – x)2 = x2 + (5)2
625 + x2 – 50x = x2 + 25
625 – 50x = 25
625 − 25 = 50x
600 = 50x
50x = 600
x = 600/50
x = 12
Hence,
BC = x = 12 cm
So, the correct answer is (D)

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.