Two pole of heights 6m and 11m stand on a plane ground. If the distance between their feet is 12m, determine the distance the distance between their poles.
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To determine the distance between the two poles, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the two poles and the distance between their feet form a right triangle.
Let's label the distance between the two poles as "x". We can label the height of the first pole as "a" (6m) and the height of the second pole as "b" (11m).
We know that the distance between their feet is 12m. This distance forms the base of the right triangle.
Using the Pythagorean theorem, we can write the equation as:
x^2 = a^2 + b^2
Substituting the given values:
x^2 = 6^2 + 11^2
x^2 = 36 + 121
x^2 = 157
Taking the square root of both sides:
x = √157
Therefore, the distance between the two poles is approximately 12.53 meters when rounded to two decimal places.
Draw a diagram. If you draw a horizontal line from the top of the 6m pole to where in intersects the 11m pole, then you have a right triangle with legs 5 and 12.
You should be able to recognize the ubiquitous 5-12-13 triangle. The tops are 13m apart.