A circus artist is climbing from the ground along a rope stretched from the top of a vertical pole and tied at the ground. The height of the pole is 12 m and the angle made by the rope with ground level is 30°.

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Question A circus artist is climbing from the ground along a rope stretched from the top of a vertical pole and tied at the ground. The height of the pole is 12 m and the angle made by the rope with ground level is 30°. Give answer to the following questionsQuestion 1 The distance covered by the artist in climbing the top of the pole is: (a) 24 m (b) 36 m (c) 28 m (d) 22 m We need to find AC
In Δ ABC
sin C = 𝐴𝐵/𝐴𝐶
sin 30° = 12/𝐴𝐶
1/2 = 12/𝐴𝐶
AC = 2 × 12
AC = 24 m
So, the correct answer is (A)
Question 2 The length of BC is: (a) 24√3 m (b) 12√3 m (c) 2√3 m (d) √3 m In Δ ABC
tan C = 𝐴𝐵/𝐵𝐶
tan 30° = 12/𝐵𝐶
1/√3 = 12/𝐵𝐶
BC = 12 × √3
BC = 12√3 m
So, the correct answer is (B)
Question 3 If sin〖(𝐴+𝐵)〗=√3/2 , then the value of (A + B) is: (a) 30° (b) 90° (c) 60° (d) 45° Given,
sin〖(𝐴+𝐵)〗=√3/2
sin〖(𝐴+𝐵)〗=sin〖60° 〗
Comparing angles
A + B = 60°
So, the correct answer is (C)
Question 4 In Δ ABC, given that ∠ A = 60° and ∠ C = 30°, then value of sin A cos C + cos C sin A is (a) 0 (b) ∞ (c) 10 (d) 3/2Now,
sin A cos C + cos C sin A
= 2 × sin A cos C
= 2 × sin 60° cos 30°
= 2 × √3/2 × √3/2
= 2 × 3/4
= 𝟑/𝟐
So, the correct answer is (B)
Question 5 Which mathematical concept is used in this problem? (a) Trigonometry (b) Triangle (c) Circle (d) MensurationIn this problem, Trigonometry is used
So, the correct answer is (A)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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