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

Last updated at April 16, 2024 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:

Question 1

The distance of AB is:

(a) 8 m (b) 6 m

(c) 5 m (d) 10 m

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:

(a) 25 cm (b) 15 cm

(c) 10 cm (d) 12 cm

Transcript

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 has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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