Two men on either side of a temple of 30 meters high observe its top at the angles of elevation 𝛼 and 𝛽 respectively. (as shown in the figure above). The distance between the two men is 40√3 meters and the distance between the first person A and the temple is 30 √3 meters. Based on the above information answer the following:

Two Men on Either Side of a Temple - Teachoo.jpg

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Question 1

∠CAB = 𝛼 =

(a)  sin -1   (2/√3)
(b)  sin -1   (1/2)
(c)  sin -1   (2)
(d)  sin -1  (√3/2)

 

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Question 2

∠CAB = 𝛼 =

(a)  cos -1   (1/5)
(b)  cos -1   (2/5)
(c)  cos -1   (√3/2)
(d)  cos -1   (4/5)

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Question 3

∠BCA = β =

(a)  tan (-1)   (1/2)
(b)  tan (-1)  (2)
(c)  tan (-1)   (1/√3)
(d)  tan (-1)  (√3)

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Question 4

∠ABC =

(a) π/4
(b) π/6
(c) π/2
(d) π/3

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Question 5

Domain and Range of cos −1 x =

(a) (−1, 1), (0 , 𝜋)
(b) [−1, 1], (0 , 𝜋)
(c) [−1, 1], [0 , 𝜋]
(d) (−1, 1), [-π/2, π/2]

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Transcript

Two men on either side of a temple of 30 meters high observe its top at the angles of elevation 𝛼 and 𝛽 respectively. (as shown in the figure above). The distance between the two men is 40√3 meters and the distance between the first person A and the temple is 30 √3 meters. Based on the above information answer the following: Question 1 ∠CAB = 𝛼 = (a) 〖𝑠𝑖𝑛〗^(−1) (2/√3) (b) 〖𝑠𝑖𝑛〗^(−1) (1/2) (c) 〖𝑠𝑖𝑛〗^(−1) (2) (d) 〖𝑠𝑖𝑛〗^(−1) (√3/2) In Δ ABD tan 𝜶 = 𝐵𝐷/𝐴𝐷 tan 𝜶 = 30/(30√3) tan 𝜶 = 1/√3 ∴ 𝜶 = 30° = 𝝅/𝟔 Thus, sin 𝜶 = sin 30° = 1/2 So, sin 𝜶 = 1/2 𝜶 = 〖𝒔𝒊𝒏〗^(−𝟏) (𝟏/𝟐) So, correct answer is (b) Question 2 ∠CAB = 𝛼 = (a) 〖𝑐𝑜𝑠〗^(−1) (1/5) (b) 〖𝑐𝑜𝑠〗^(−1) (2/5) (c) 〖𝑐𝑜𝑠〗^(−1) (√3/2) (d) 〖𝑐𝑜𝑠〗^(−1) (4/5) Now, 𝜶 = 30° = 𝝅/𝟔 Thus, cos 𝜶 = cos 30° = √3/2 So, sin 𝜶 =√3/2 𝜶 = 〖𝑐𝑜𝑠〗^(−1) (√3/2) So, correct answer is (c) Question 3 ∠BCA = 𝛽 = (a) 〖𝑡𝑎𝑛〗^(−1) (1/2) (b) 〖𝑡𝑎𝑛〗^(−1) (2) (c) 〖𝑡𝑎𝑛〗^(−1) (1/√3) (d) 〖𝑡𝑎𝑛〗^(−1) (√3) In Δ ABD tan 𝛽 = 𝐵𝐷/𝐴𝐷 tan 𝛽 = 30/(10√3) tan 𝛽 = 3/√3 tan 𝛽 = √3 𝛽 = 〖𝑡𝑎𝑛〗^(−1) (√3) So, the correct answer is (d) Also, 𝛽 = 60° = 𝝅/𝟑 Question 4 ∠ABC = (a) 𝜋/4 (b) 𝜋/6 (c) 𝜋/2 (d) 𝜋/3 Since 𝜶 = 30° and 𝛽 = 60° In Δ ABC, By Angle sum property 𝜶 + 𝛽 + ∠ ABC = 180° 30° + 60° + ∠ ABC = 180° ∠ ABC = 90° ∠ ABC = 𝝅/𝟐 So, the correct answer is (c) Question 5 Domain and Range of cos−1 𝑥 = (a) (−1, 1), (0 , 𝜋) (b) [−1, 1], (0 , 𝜋) (c) [−1, 1], [0 , 𝜋] (d) (−1, 1), [−𝜋/2, 𝜋/2] Since cos x is defined at x = 0, and x = 𝜋 Domain of cos−1 𝑥 includes −1 and 1 Range of cos−1 𝑥 also includes 0 and 𝜋 So, the correct answer is (c)

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.