Question

A palm wine tapper climbs to point on a palm tree 9 m above the uses a ladder 10 m long ,which is leaning against the palm tree. Calculate the distance of the foot of the ladder from the foot of the palm tree​.

Answer 1

Using the Pythagorean theorem and given the lengths of the ladder (10 m) and the height reached on the tree (9 m), the distance from the foot of the ladder to the foot of the palm tree is approximately 4.36 meters.

Step-by-step explanation:

To find the distance of the foot of the ladder from the foot of the palm tree, we can use the Pythagorean theorem. This theorem relates the lengths of the sides of a right-angled triangle where the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse).

In this case, we have a right-angled triangle where the palm tree and the ground form the two shorter sides, and the ladder is the hypotenuse. We are given that the length of the ladder (hypotenuse) is 10 m and the height of the point on the tree where the ladder reaches (one of the shorter sides) is 9 m. Using the Pythagorean theorem (a^2 + b^2 = c^2), we can calculate the distance from the foot of the ladder to the foot of the tree (b).

Let's denote the height of the palm tree as 'a' and the distance from the foot of the ladder to the tree as 'b'. So we have:

a^2 + b^2 = c^2
9^2 + b^2 = 10^2
81 + b^2 = 100
b^2 = 100 - 81
b^2 = 19
b = √19
b ≈ 4.36 m

So, the distance of the foot of the ladder from the foot of the palm tree is approximately 4.36 meters.