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A tower stands on the top of a building which is 40 metres high. The angles of depression of a point situated on the ground from the top and the bottom of the tower are found to be 60° and 45° respectively. What is the height (in metres) of the tower?
- a)20√3
- b)30(√3 + 1)
- c)40(√3 - 1)
- d)50(√3 - 1)
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A tower stands on the top of a building which is 40 metres high. The a...
Let the height of the tower be H mtr
tan45° = 40/AB
⇒ AB = 40 mtr
And tan60° = (H + 40) /AB
⇒ √3 = (H + 40) /40
tan45° = 40/AB
⇒ AB = 40 mtr
And tan60° = (H + 40) /AB
⇒ √3 = (H + 40) /40
Most Upvoted Answer
A tower stands on the top of a building which is 40 metres high. The a...
Given information:
- Height of the building = 40 metres
- Angle of depression from top of the tower to a point on the ground = 60°
- Angle of depression from bottom of the tower to the same point on the ground = 45°
Approach:
1. Use trigonometry to find the height of the tower.
2. Set up equations using tangent function for both angles of depression.
3. Solve the equations to find the height of the tower.
Calculations:
Let the height of the tower be h metres.
From the angle of depression of 60°:
tan 60° = h / x
√3 = h / x
x = h / √3
From the angle of depression of 45°:
tan 45° = (h + 40) / x
1 = (h + 40) / (h / √3)
√3 = h + 40 / h
√3h = h + 40
√3h - h = 40
h(√3 - 1) = 40
h = 40 / (√3 - 1)
h = 40(√3 + 1) / (√3 - 1)
h = 40(√3 + 1)(√3 + 1) / ((√3 - 1)(√3 + 1))
h = 40(3 + 2√3 + 1) / (3 - 1)
h = 40(4 + 2√3)
h = 160 + 80√3
Therefore, the height of the tower is 40(√3 - 1) metres, which corresponds to option C.
- Height of the building = 40 metres
- Angle of depression from top of the tower to a point on the ground = 60°
- Angle of depression from bottom of the tower to the same point on the ground = 45°
Approach:
1. Use trigonometry to find the height of the tower.
2. Set up equations using tangent function for both angles of depression.
3. Solve the equations to find the height of the tower.
Calculations:
Let the height of the tower be h metres.
From the angle of depression of 60°:
tan 60° = h / x
√3 = h / x
x = h / √3
From the angle of depression of 45°:
tan 45° = (h + 40) / x
1 = (h + 40) / (h / √3)
√3 = h + 40 / h
√3h = h + 40
√3h - h = 40
h(√3 - 1) = 40
h = 40 / (√3 - 1)
h = 40(√3 + 1) / (√3 - 1)
h = 40(√3 + 1)(√3 + 1) / ((√3 - 1)(√3 + 1))
h = 40(3 + 2√3 + 1) / (3 - 1)
h = 40(4 + 2√3)
h = 160 + 80√3
Therefore, the height of the tower is 40(√3 - 1) metres, which corresponds to option C.
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Community Answer
A tower stands on the top of a building which is 40 metres high. The a...
Let the height of the tower be H mtr
tan45° = 40/AB
⇒ AB = 40 mtr
And tan60° = (H + 40) /AB
⇒ √3 = (H + 40) /40
tan45° = 40/AB
⇒ AB = 40 mtr
And tan60° = (H + 40) /AB
⇒ √3 = (H + 40) /40
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A tower stands on the top of a building which is 40 metres high. The angles of depression of a point situated on the ground from the top and the bottom of the tower are found to be 60° and 45° respectively. What is the height (in metres) of the tower?a)20√3b)30(√3 + 1)c)40(√3 - 1)d)50(√3 - 1)Correct answer is option 'C'. Can you explain this answer?
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A tower stands on the top of a building which is 40 metres high. The angles of depression of a point situated on the ground from the top and the bottom of the tower are found to be 60° and 45° respectively. What is the height (in metres) of the tower?a)20√3b)30(√3 + 1)c)40(√3 - 1)d)50(√3 - 1)Correct answer is option 'C'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about A tower stands on the top of a building which is 40 metres high. The angles of depression of a point situated on the ground from the top and the bottom of the tower are found to be 60° and 45° respectively. What is the height (in metres) of the tower?a)20√3b)30(√3 + 1)c)40(√3 - 1)d)50(√3 - 1)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A tower stands on the top of a building which is 40 metres high. The angles of depression of a point situated on the ground from the top and the bottom of the tower are found to be 60° and 45° respectively. What is the height (in metres) of the tower?a)20√3b)30(√3 + 1)c)40(√3 - 1)d)50(√3 - 1)Correct answer is option 'C'. Can you explain this answer?.
A tower stands on the top of a building which is 40 metres high. The angles of depression of a point situated on the ground from the top and the bottom of the tower are found to be 60° and 45° respectively. What is the height (in metres) of the tower?a)20√3b)30(√3 + 1)c)40(√3 - 1)d)50(√3 - 1)Correct answer is option 'C'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about A tower stands on the top of a building which is 40 metres high. The angles of depression of a point situated on the ground from the top and the bottom of the tower are found to be 60° and 45° respectively. What is the height (in metres) of the tower?a)20√3b)30(√3 + 1)c)40(√3 - 1)d)50(√3 - 1)Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A tower stands on the top of a building which is 40 metres high. The angles of depression of a point situated on the ground from the top and the bottom of the tower are found to be 60° and 45° respectively. What is the height (in metres) of the tower?a)20√3b)30(√3 + 1)c)40(√3 - 1)d)50(√3 - 1)Correct answer is option 'C'. Can you explain this answer?.
Solutions for A tower stands on the top of a building which is 40 metres high. The angles of depression of a point situated on the ground from the top and the bottom of the tower are found to be 60° and 45° respectively. What is the height (in metres) of the tower?a)20√3b)30(√3 + 1)c)40(√3 - 1)d)50(√3 - 1)Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for SSC.
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