The heights of two towers are 90 meters and 45 meters. The line joining their tops make an angle 450 with the horizontal then the distance between the two towers is
Question
The heights of two towers are 90 meters and 45 meters. The line joining their tops make an angle 450 with the horizontal then the distance between the two towers is
Solution
To solve this problem, we can use trigonometry. Here are the steps:
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First, we need to find the height difference between the two towers. The height of the first tower is 90 meters and the height of the second tower is 45 meters. So, the difference is 90 - 45 = 45 meters.
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The problem states that the line joining the tops of the towers makes an angle of 45 degrees with the horizontal. In a right triangle, the tangent of an angle is equal to the opposite side (height difference) divided by the adjacent side (distance between the towers).
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So, we can set up the equation tan(45) = 45 / d, where d is the distance between the towers.
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The tangent of 45 degrees is 1, so the equation simplifies to 1 = 45 / d.
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Solving for d, we get d = 45 meters.
So, the distance between the two towers is 45 meters.
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