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vichka [17]
3 years ago
8

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

Mathematics
1 answer:
Ksenya-84 [330]3 years ago
5 0

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,

(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 \sqrt{864}=x

\Rightarrow \sqrt{864}=x

\Rightarrow 29.39=x

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

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