Question

how high up a vertical wall will a 30-foot ladder reach if the foot of the ladder is placed 6 feet from the wall

Answer 1

The height of wall where 30-foot ladder reaches is 29.39 foot.

Explanation:

Consider a triangle ABC showing AC be the 30 foot ladder that is resting on a wall AB and foot of ladder is 6 foot from the wall that is BC = 6

We have to find the height of wall where ladder is reaching.

Since building and foot of ladder makes a right angle at B.

Let AB be x foot.

PYTHAGORAS THEOREM STATES THAT THE SUM OF SQUARE OF BASE AND PERPENDICULAR IS EQUAL TO THE THE SQUARE OF HYPOTENUSE.

Applying Pythagoras theorem,

`(AC)^2=(AB)^2+(BC)^2`

`\Rightarrow (30)^2=(x)^2+(6)^2`

`\Rightarrow 900=(x)^2+36`

`\Rightarrow 900-36=x^2`

`\Rightarrow 864=x^2`

`\Rightarrow √(864)=x`

`\Rightarrow √(864)=x`

`\Rightarrow 29.39=x`

Thus, the height of wall where 30-foot ladder reaches is 29.39 foot.