Question

How far from the base of the house do you need to place a 15 foot ladder so that it exactly reaches the top of a 12 foot wall?

Answer 1

Answer:

9 ft

Step-by-step explanation:

The ladder is 15 foot

The height the ladder reaches from the bottom of the wall is 12 ft

The distance (x) from the bottom of the wall to the foot of the ladder is:

Applying the Pythagorean theorem;

x = $\sqrt{15^2 - 12^2}$ = 9 ft

Answer 2

A 15 foot ladder needs to be placed at a distance of 9 foot from the base of the house so that it exactly reaches the top of a 12 foot wall.

Further Explanation:

Right triangle

• A right triangle is a triangle with one of its angles being 90 degrees or right angle.
• The triangle has two shorter sides making the right angle and the hypotenuse which is the longest side.

Scalene triangle

• It is a triangle that with sides and angles that are not equal.

Pythagoras Rule

• According to Pythagoras rule, in a right angled triangle if the squares of the shorter sides are added then they are equivalent to the square of the hypotenuse.
• That is; $a^{2} + b^{2} =c^{2}$, where a and b are the shorter sides while c is the hypotenuse.

In this case;

• The ladder, the wall of the house and the ground from the base of the house makes a right angled triangle;

Therefore;

• Length of the ladder is the hypotenuse which is 15 ft
• The wall of the house is one of the leg which is 12 ft

We are going to find the distance of the ladder from the base of the house on the ground which is the other leg.

Using Pythagoras theorem;

$a^{2} + b^{2} = c^{2}$

Taking the horizontal distance of the ladder from the wall as b

Then;

$b^{2} = c^{2} -a^{2}$

therefore,

$b^{2} = 15^{2} -12^{2}$

$b^{2} = 225 -144$

$b^{2} = 81$

$b = \sqrt{81} \\b= 9 ft$

Hence; the ladder needs to be placed at a distance of 9 foot from the base of the house.

Keywords: Right triangle, Pythagoras rule

Learn more about:

• Pythagoras theorem: brainly.com/question/13035995
• Right triangle: brainly.com/question/13035995

• Application of Pythagoras theorem: https://brainly.com/question/11638432

Level; High school

Subject: Mathematics

Topic: Pythagoras theorem