Question 3Two buildings are 1010 m apart. If the taller building is 100100 m tall and a cable of length 22.422.4 m connects the top of the two towers, what is the height of the shorter building?
Question
Question 3Two buildings are 1010 m apart. If the taller building is 100100 m tall and a cable of length 22.422.4 m connects the top of the two towers, what is the height of the shorter building?
Solution
To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Here, we have a right triangle formed by the taller building, the cable, and the line segment from the top of the shorter building to the point directly below the top of the taller building.
The length of the cable is the hypotenuse of the triangle, the height of the taller building is one of the sides, and the difference in height between the two buildings is the other side.
We can set up the equation as follows:
(height of taller building)^2 + (distance between buildings)^2 = (length of cable)^2
Substituting the given values:
(100)^2 + (10)^2 = (22.4)^2
10000 + 100 = 501.76
Subtract 100 from both sides:
10000 = 501.76 - 100
10000 = 401.76
Now, we need to find the height of the shorter building. We know that the height of the taller building is 100 m, so the height of the shorter building is:
100 - √401.76
= 100 - 20.044
= 79.956 m
So, the height of the shorter building is approximately 79.956 m.
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