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A man using a theodolite stands some distance away from 80m high control tower and measured it's angle of elevation as 48 degrees.1.how far away from the tower is he if the theodolite stands 1.5m above the ground. 2. if the man now moves 110m away from the tower ,what is the angle of elevation at that point?
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A man using a theodolite stands some distance away from 80m high contr...
Answer:
1. Distance from the tower
- Let's assume that the man is standing at a distance of x meters away from the control tower.
- From the given information, we know that the height of the control tower is 80m and the angle of elevation is 48 degrees.
- The angle of elevation is the angle between the horizontal and the line of sight to the top of the tower.
- Therefore, we can draw a right-angled triangle with the height of the tower (80m) as the opposite side and the distance from the tower (x + 1.5m) as the adjacent side.
- The tangent of the angle of elevation is equal to the opposite side divided by the adjacent side.
- So, tan(48) = 80 / (x + 1.5)
- Solving for x, we get x = 79.5m (approx.)
- Therefore, the man is standing at a distance of approximately 79.5m away from the control tower.
2. Angle of elevation at 110m away from the tower
- Now, let's assume that the man has moved 110m away from the tower.
- We need to find the new angle of elevation from this point.
- Again, we can draw a right-angled triangle with the height of the tower (80m) as the opposite side and the new distance from the tower (110 + 1.5m) as the adjacent side.
- The tangent of the new angle of elevation is equal to the opposite side divided by the adjacent side.
- So, tan(theta) = 80 / 111.5
- Solving for theta, we get theta = 37.6 degrees (approx.)
- Therefore, the new angle of elevation from this point is approximately 37.6 degrees.
Conclusion:
- The man is standing at a distance of approximately 79.5m away from the control tower.
- The new angle of elevation from a point 110m away from the tower is approximately 37.6 degrees.
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A man using a theodolite stands some distance away from 80m high control tower and measured it's angle of elevation as 48 degrees.1.how far away from the tower is he if the theodolite stands 1.5m above the ground. 2. if the man now moves 110m away from the tower ,what is the angle of elevation at that point?
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A man using a theodolite stands some distance away from 80m high control tower and measured it's angle of elevation as 48 degrees.1.how far away from the tower is he if the theodolite stands 1.5m above the ground. 2. if the man now moves 110m away from the tower ,what is the angle of elevation at that point? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A man using a theodolite stands some distance away from 80m high control tower and measured it's angle of elevation as 48 degrees.1.how far away from the tower is he if the theodolite stands 1.5m above the ground. 2. if the man now moves 110m away from the tower ,what is the angle of elevation at that point? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man using a theodolite stands some distance away from 80m high control tower and measured it's angle of elevation as 48 degrees.1.how far away from the tower is he if the theodolite stands 1.5m above the ground. 2. if the man now moves 110m away from the tower ,what is the angle of elevation at that point?.
A man using a theodolite stands some distance away from 80m high control tower and measured it's angle of elevation as 48 degrees.1.how far away from the tower is he if the theodolite stands 1.5m above the ground. 2. if the man now moves 110m away from the tower ,what is the angle of elevation at that point? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about A man using a theodolite stands some distance away from 80m high control tower and measured it's angle of elevation as 48 degrees.1.how far away from the tower is he if the theodolite stands 1.5m above the ground. 2. if the man now moves 110m away from the tower ,what is the angle of elevation at that point? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A man using a theodolite stands some distance away from 80m high control tower and measured it's angle of elevation as 48 degrees.1.how far away from the tower is he if the theodolite stands 1.5m above the ground. 2. if the man now moves 110m away from the tower ,what is the angle of elevation at that point?.
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