Question

A 15-foot pole is leaning against a tree. The bottom of the pole is 8 feet away from the bottom of the tree. Approximately how high up the tree does the top of the pole reach? 1. 9 feet 7. 0 feet 12. 7 feet 17. 0 feet.

Answer 1

Poles are usually standing vertical, thus at right angle with the ground. The length of tree touching the top of pole is given by: Option D: 17 feet.

What is a right angled triangle?

A right angled triangle is a triangle having one of its angle with measure of 90 degrees.

The slant side(leaning side) of that triangle is called Hypotenuse and it is the longest side in that triangle.

What is Pythagoras Theorem?

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

$|AC|^2 = |AB|^2 + |BC|^2$

Where |AB| = length of line segment AB.

We can use the fact that the pole is standing vertical, the tree is leaning on it, so there is right angled triangle formation, and thus, we can use Pythagoras theorem.

Consider the graph attached below.

The tree is AC, The pole is AB and the distance of pole's bottom from the bottom of the tree is denoted by length of BC

We're already given that:

Pole length = |AB| = 15 feet

Distance between bottom of pole to bottom of tree = |BC| = 8 feet

The length of tree is |AC| = x feet (assume)

Then, by the Pythagoras theorem, we get:

$x^2 = 15^2 + 8^2\\\\x = \sqrt{225 + 64} \text{\: (We took positive root since length is a non negative quantity)}\\\\x =\sqrt{289} = 17 \: \rm feet$

Thus, length of AC = |AC| = 17 feet.

Thus,

The length of tree touching the top of pole is given by: Option D: 17 feet.

Learn more about Pythagoras theorem here:

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