Two vertical poles 20 meterd and 30 metrrd high, are 60 meters apart. A rope is to be attached from the top of one pole to a point on the ground half-way between the poles and then to the top of other pole. How long a rope is needed?
Draw a diagram. You have two right triangles with legs
20,30 and 30,30
The rope length is the sum of the two hypotenuses:
√(20^2+30^2) + √(30^2+30^2)
= 10√13 + 30√2
You can help
To find the length of the rope needed, we can use the Pythagorean theorem.
Let's assume the point on the ground where the rope is attached is point A. The distance from point A to the top of the shorter pole (20 meters high) is 10 meters, as it is halfway between the two poles.
Now, let's label the top of the shorter pole as point B and the top of the taller pole as point C. The distance between points B and C is given as 60 meters.
Using the Pythagorean theorem, we can find the length of the rope, which is the hypotenuse of the right triangle formed by points A, B, and C.
The equation for the Pythagorean theorem is:
AB^2 + BC^2 = AC^2
Substituting the values we know:
10^2 + 60^2 = AC^2
100 + 3600 = AC^2
3700 = AC^2
Taking the square root of both sides:
AC ≈ √3700
AC ≈ 60.83 meters
Therefore, a rope of approximately 60.83 meters is needed to connect the tops of the two poles.
To find the length of the rope needed, we can use the Pythagorean theorem.
First, let's draw a diagram to visualize the situation:
```
A
/|
/ |
/ |
20m / | 30m
/ |
/ |
/______|
60m
```
In the diagram, A represents the point on the ground where the rope is attached.
Now, let's calculate the length of the rope needed.
We have a right triangle, where the hypotenuse is the length of the rope and the two legs are the distances from point A to the top of each pole.
By the Pythagorean theorem, the square of the length of the hypotenuse is equal to the sum of the squares of the legs.
Using this information, we can calculate the length of the rope:
Length of the hypotenuse^2 = Length of the first leg^2 + Length of the second leg^2
Length of the hypotenuse^2 = (20m)^2 + (30m)^2
Length of the hypotenuse^2 = 400m^2 + 900m^2
Length of the hypotenuse^2 = 1300m^2
Length of the hypotenuse = √1300m^2
Length of the hypotenuse ≈ 36.055 meters
Therefore, the length of the rope needed is approximately 36.055 meters.