Question

A 11m long ladder is placed against a tree. the top of the ladder reaches a point 10m up to the tree

how far away is the base of the ladder from the base of the tree?
give your answer in metres(m) in 1 d.p

Answer 1

The distance between the base of the ladder and the base of the tree is approximately 4.6m.

Step-by-step explanation:

To find the distance between the base of the ladder and the base of the tree, we can use the Pythagorean theorem. The ladder, tree, and the ground form a right triangle where the length of the ladder is the hypotenuse. We have the length of the ladder as 11m and the height of the tree as 10m.

Let x be the distance between the base of the ladder and the base of the tree. Using the Pythagorean theorem, we have:

x^2 + 10^2 = 11^2

Simplifying the equation:

x^2 + 100 = 121

x^2 = 121 - 100

x^2 = 21

x = sqrt(21)

So, the distance between the base of the ladder and the base of the tree is approximately 4.6m.