Question

A 10 m. long ladder is placed against a wall. It is inclined at an angle of 45° to the ground. Find the distance of the foot of the ladder from the wall.

Answer 1

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Answer 2

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

$\green{\therefore{\text{Distance\:between\:wall\:and\:foot\:of\:ladder=}5\sqrt{2}\:m}}$

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

• In the given question information given about a 10 m long ladder is placed against a wall. It is inclined at an angle of 45° to the ground.

• We have to find the distance of the foot of the ladder from the wall.

$\green{\underline \bold{Given :}} \\ : \implies \text{Length\:of\:ladder= 10\:m} \\ \\ : \implies \text{Angle\:of\:elevation=}45^{\circ}\\\\ \red{\underline \bold{To \: Find:}} \\ : \implies \text{Distance\:between\:wall\:and\:foot\:of\:ladder= ?}$

• Accroding to given question :

$\bold{In \: \triangle \: ABC} \\ : \implies cos \: \theta = \frac{\text{Base}}{\text{Hypotenuse}} \\ \\ : \implies cos\: 45^{\circ}= \frac{BC}{AC} \\ \\ : \implies \frac{1}{\sqrt{2}}= \frac{BC}{10} \\ \\ : \implies BC= \frac{10}{\sqrt{2}}\ \\ \\ \green{ : \implies {BC=5\sqrt{2}\:m}}\\\\ \green{\therefore{\text{Distance\:between\:wall\:and\:foot\:of\:ladder=}5\sqrt{2}\:m}}$