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Two men on either side of a tower 75 m high observe the angle of elevation of the top of the tower to be 30° and 60°. What is the distance between two men?
- a)100√3 m
- b)75√3 m
- c)100√3/3 m
- d)60√3 m
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Two men on either side of a tower 75 m high observe the angle of eleva...
In the figure, AB is the tower and CD is the distance between two men on either side of tower;
In ΔABD
tan 60° = AB/AD
⇒ √3 = 75/AD
⇒ AD = 75/√3
tan 30° = AB/AC
⇒ 1/√3 = 75/AC
⇒ AC = 75√3
∴ CD = 75√3 + 75/√3 = 75√3 + 25√3 = 100√3
∴ Distance between two men on either side of tower = 100√3 m
Most Upvoted Answer
Two men on either side of a tower 75 m high observe the angle of eleva...
Let's call the two men A and B.
From the information given, we can draw a diagram where the tower is represented by a vertical line and the angles of elevation are measured from the horizontal ground level to the top of the tower.
Let the distance of man A from the tower be x meters and the distance of man B from the tower be y meters.
According to the information given, the angle of elevation from man A is 30 degrees and the angle of elevation from man B is also 30 degrees.
Now, we can form a right triangle with the tower as the vertical side, the distance from man A to the tower as the base, and the distance from man B to the tower as the hypotenuse.
Since the angles of elevation are the same, the two right triangles are similar. Therefore, we can set up the following proportions:
tan(30) = 75/x
tan(30) = 75/y
Solving for x and y, we get:
x = 75/tan(30) = 75/(√3/3) = 75√3
x ≈ 43.3 m
y = 75/tan(30) = 75/(√3/3) = 75√3
y ≈ 43.3 m
Therefore, man A is approximately 43.3 m away from the tower and man B is also approximately 43.3 m away from the tower.
From the information given, we can draw a diagram where the tower is represented by a vertical line and the angles of elevation are measured from the horizontal ground level to the top of the tower.
Let the distance of man A from the tower be x meters and the distance of man B from the tower be y meters.
According to the information given, the angle of elevation from man A is 30 degrees and the angle of elevation from man B is also 30 degrees.
Now, we can form a right triangle with the tower as the vertical side, the distance from man A to the tower as the base, and the distance from man B to the tower as the hypotenuse.
Since the angles of elevation are the same, the two right triangles are similar. Therefore, we can set up the following proportions:
tan(30) = 75/x
tan(30) = 75/y
Solving for x and y, we get:
x = 75/tan(30) = 75/(√3/3) = 75√3
x ≈ 43.3 m
y = 75/tan(30) = 75/(√3/3) = 75√3
y ≈ 43.3 m
Therefore, man A is approximately 43.3 m away from the tower and man B is also approximately 43.3 m away from the tower.
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