2 poles of height 15m and 20m stand vertically upstraight on a plane ground. If the distance between their feet is 12m. Find the distance between their tops ?
they are 5m apart in height
Use the Pythagorean Theorem to find the hypotenuse.
Learn to recognize a few basic triangles, such as this one, which is 5-12-13
To find the distance between the tops of the two poles, we can use the concept of similar triangles.
Let's denote the height of the first pole as h1, the height of the second pole as h2, and the distance between their feet as d.
In this case, h1 = 15m, h2 = 20m, and d = 12m.
Since the poles are standing vertically upright, we can create two right-angled triangles:
Triangle A: base = d, height = h1
Triangle B: base = d, height = h2
These two triangles are similar because they share the same angles.
By using the property of similar triangles, we know that the ratio of the heights of similar triangles is equal to the ratio of their bases.
Therefore, we can set up the following proportion:
h1 / d = h2 / x
Where x represents the distance between the tops of the two poles.
Now, we can substitute the given values into the proportion:
15 / 12 = 20 / x
To solve for x, we can cross-multiply:
15x = 12 * 20
15x = 240
Divide both sides by 15:
x = 240 / 15
x = 16
Therefore, the distance between the tops of the two poles is 16 meters.