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Two observers are stationed due north of a tower (of height x meter) at a distance y meter from each other. The angles of elevation of the tower observed by them are 30° and 45° respectively. Then x/y is equal to
- a)(√2 – 1) /2
- b)(√3 – 1) /2
- c)(√3 + 1) /2
- d)1
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Two observers are stationed due north of a tower (of height x meter) a...
In triangle ABC
tan∠ACB = AB/BC
⇒ tan45° = x/BC
⇒ 1 = x/BC
⇒ x = BC
In triangle ABD
tan∠ADB = AB/BD
⇒ tan30° = x/BD
⇒ 1/√3 = x/BD
⇒ BD = x√3
CD = BD – BC
⇒ y = x(√3 – 1)
⇒ y(√3 + 1) = x × (√3 – 1) × (√3 + 1)
⇒ y(√3 + 1) = x × (3 – 1) [∵ (a – b) (a + b) = a2 – b2]
⇒ y(√3 + 1) = 2x
∴ x/y = (√3 + 1) /2
tan∠ACB = AB/BC
⇒ tan45° = x/BC
⇒ 1 = x/BC
⇒ x = BC
In triangle ABD
tan∠ADB = AB/BD
⇒ tan30° = x/BD
⇒ 1/√3 = x/BD
⇒ BD = x√3
CD = BD – BC
⇒ y = x(√3 – 1)
⇒ y(√3 + 1) = x × (√3 – 1) × (√3 + 1)
⇒ y(√3 + 1) = x × (3 – 1) [∵ (a – b) (a + b) = a2 – b2]
⇒ y(√3 + 1) = 2x
∴ x/y = (√3 + 1) /2
Most Upvoted Answer
Two observers are stationed due north of a tower (of height x meter) a...
Let the height of the tower be x meters and the distance between the observers be y meters.
From the first observer's position, the angle of elevation to the top of the tower is 30 degrees. This forms a right-angled triangle with the height of the tower, the distance from the observer to the base of the tower, and the line of sight to the top of the tower.
Therefore, we can write:
tan(30 degrees) = x / y
1/sqrt(3) = x / y
y = sqrt(3) * x
Similarly, from the second observer's position, the angle of elevation to the top of the tower is also 30 degrees. This forms another right-angled triangle with the height of the tower, the distance from the second observer to the base of the tower, and the line of sight to the top of the tower.
Therefore, we can write:
tan(30 degrees) = x / (y + d)
1/sqrt(3) = x / (sqrt(3) * x + d)
1/sqrt(3) = 1 + d / sqrt(3) * x
d = (sqrt(3) - 1) * x
So, the distance between the two observers is (sqrt(3) - 1) * x meters.
From the first observer's position, the angle of elevation to the top of the tower is 30 degrees. This forms a right-angled triangle with the height of the tower, the distance from the observer to the base of the tower, and the line of sight to the top of the tower.
Therefore, we can write:
tan(30 degrees) = x / y
1/sqrt(3) = x / y
y = sqrt(3) * x
Similarly, from the second observer's position, the angle of elevation to the top of the tower is also 30 degrees. This forms another right-angled triangle with the height of the tower, the distance from the second observer to the base of the tower, and the line of sight to the top of the tower.
Therefore, we can write:
tan(30 degrees) = x / (y + d)
1/sqrt(3) = x / (sqrt(3) * x + d)
1/sqrt(3) = 1 + d / sqrt(3) * x
d = (sqrt(3) - 1) * x
So, the distance between the two observers is (sqrt(3) - 1) * x meters.
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Two observers are stationed due north of a tower (of height x meter) at a distance y meter from each other. The angles of elevation of the tower observed by them are 30° and 45° respectively. Then x/y is equal toa)(√2 – 1) /2b)(√3 – 1) /2c)(√3 + 1) /2d)1Correct answer is option 'C'. Can you explain this answer?
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Two observers are stationed due north of a tower (of height x meter) at a distance y meter from each other. The angles of elevation of the tower observed by them are 30° and 45° respectively. Then x/y is equal toa)(√2 – 1) /2b)(√3 – 1) /2c)(√3 + 1) /2d)1Correct answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Two observers are stationed due north of a tower (of height x meter) at a distance y meter from each other. The angles of elevation of the tower observed by them are 30° and 45° respectively. Then x/y is equal toa)(√2 – 1) /2b)(√3 – 1) /2c)(√3 + 1) /2d)1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two observers are stationed due north of a tower (of height x meter) at a distance y meter from each other. The angles of elevation of the tower observed by them are 30° and 45° respectively. Then x/y is equal toa)(√2 – 1) /2b)(√3 – 1) /2c)(√3 + 1) /2d)1Correct answer is option 'C'. Can you explain this answer?.
Two observers are stationed due north of a tower (of height x meter) at a distance y meter from each other. The angles of elevation of the tower observed by them are 30° and 45° respectively. Then x/y is equal toa)(√2 – 1) /2b)(√3 – 1) /2c)(√3 + 1) /2d)1Correct answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Two observers are stationed due north of a tower (of height x meter) at a distance y meter from each other. The angles of elevation of the tower observed by them are 30° and 45° respectively. Then x/y is equal toa)(√2 – 1) /2b)(√3 – 1) /2c)(√3 + 1) /2d)1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two observers are stationed due north of a tower (of height x meter) at a distance y meter from each other. The angles of elevation of the tower observed by them are 30° and 45° respectively. Then x/y is equal toa)(√2 – 1) /2b)(√3 – 1) /2c)(√3 + 1) /2d)1Correct answer is option 'C'. Can you explain this answer?.
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Two observers are stationed due north of a tower (of height x meter) at a distance y meter from each other. The angles of elevation of the tower observed by them are 30° and 45° respectively. Then x/y is equal toa)(√2 – 1) /2b)(√3 – 1) /2c)(√3 + 1) /2d)1Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Two observers are stationed due north of a tower (of height x meter) at a distance y meter from each other. The angles of elevation of the tower observed by them are 30° and 45° respectively. Then x/y is equal toa)(√2 – 1) /2b)(√3 – 1) /2c)(√3 + 1) /2d)1Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Two observers are stationed due north of a tower (of height x meter) at a distance y meter from each other. The angles of elevation of the tower observed by them are 30° and 45° respectively. Then x/y is equal toa)(√2 – 1) /2b)(√3 – 1) /2c)(√3 + 1) /2d)1Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
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