Question

a 13 foot ladder is leaning against a vertical wall . The lowest point of the ladder is 4 feet from the wall. what is the height of the point where the ladder touches the wall ? (Round your answer to the nearest tenth of a foot.)​

Answer 1

Length of ladder = hypotenuse

H^2=p^2+b^2

13^2=p^2+4^2

169=p^2+16

P^2=153

P=√153

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\therefore{\text{Height\:of\:wall=12.36\:feet}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

• In the given question information given about a 13 foot ladder is leaning against a vertical wall . The lowest point of the ladder is 4 feet from the wall.

• We have to find the height of the point where the ladder touches the wall.

$\green{\underline \bold{Given :}} \\ : \implies \text{Length\:of\:ladder=13\:feet} \\ \\ : \implies \text{Distance\:between\:wall\:and\:foot\:of\:ladder=4\:feet}\\\\ \red{\underline \bold{To \: Find:}} \\ : \implies \text{Height\:of\:wall= ?}$

• Accroding to given question :

$\bold{ By \: pythagoras \: theorem} \\ : \implies {h}^{2} = {p}^{2} + {b}^{2} \\ \\ : \implies {AC}^{2} = {AB}^{2} + {BC}^{2} \\ \\ : \implies {13}^{2} = {AB}^{2} + 4^{2} \\ \\ : \implies {AB}^{2} =169-16\\ \\ : \implies {AB}^{2} =153 \\ \\ : \implies AB= \sqrt{153} \\ \\ \green{: \implies \text{AB = 12.36\: feet}}$