Answer:
The height of wall where 30-foot ladder reaches is 29.39 foot.
Step-by-step 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,
[tex](AC)^2=(AB)^2+(BC)^2[/tex]
[tex]\Rightarrow (30)^2=(x)^2+(6)^2[/tex]
[tex]\Rightarrow 900=(x)^2+36[/tex]
[tex]\Rightarrow 900-36=x^2[/tex]
[tex]\Rightarrow 864=x^2[/tex]
[tex]\Rightarrow \sqrt{864}=x[/tex]
[tex]\Rightarrow \sqrt{864}=x[/tex]
[tex]\Rightarrow 29.39=x[/tex]
Thus, the height of wall where 30-foot ladder reaches is 29.39 foot.
