a washing line is attached at points A and B on two vertical posts standing horizontal ground. Point A is 2.1 meters above the ground on one post. Point B is 1.7 meters above the ground on the other post. The horizontal distance between the two posts is 6 meters. Calculate the distance AB
difference in height = 2.1 - 1.7 = 0.4
right triangle base = 6, height = 0.4
so
hypotenuse = sqrt( 0.16 +36) = 6.013
just use stretchy clothesline 6 m long :)
To calculate the distance AB, we can use the Pythagorean theorem since we have a right-angled triangle.
Let's label the distance between the two posts as 'd' and the distance AB as 'x'.
According to the problem, point A is 2.1 meters above the ground, and point B is 1.7 meters above the ground. This creates a vertical difference of 2.1 - 1.7 = 0.4 meters.
Now, let's divide our problem into two right-angled triangles. Triangle ABC, where AB is the hypotenuse, and triangle ADB, where AD is the hypotenuse.
Using triangle ABC:
We know the vertical difference is 0.4 meters, and the horizontal distance between the two posts is 6 meters.
Using the Pythagorean theorem: (AB)^2 = (BC)^2 + (AC)^2
Substituting the values we know: (AB)^2 = 6^2 + 0.4^2
Simplifying the equation:
(AB)^2 = 36 + 0.16
(AB)^2 = 36.16
Now, let's calculate the square root of both sides:
AB = sqrt(36.16)
AB ≈ 6.01 meters
Therefore, the distance AB is approximately 6.01 meters.