Question

A ladder makes an angle of 30degree with a wall. If the foot of the ladder is 5m away from the wall,find the length of the ladder.

Answer 1

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Answer 2

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

$\green{\therefore{\text{Length\:of\:ladder=10\:m}}}$

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

• In the given question information given about angle of elevation of a ladder to wall is 60° and the foot of the ladder 5 m away the wall.

• We have to Find the length of ladder.

$\green{\underline \bold{Given :}} \\ : \implies \text{Distance \: between\: ladder \:and\:wall= 5\:m} \\ \\ : \implies \text{Angle\:of\:elevation\:of\:ladder\:to\:wall= 60\degree} \\ \\ \red{\underline \bold{To \: Find:}} \\ : \implies \text{Length\:of\: ladder = ?}$

• Accroding to given question :

$\bold{In \: \triangle \: ABC} \\ : \implies cos\:\theta=\frac{\text{Base}}{\text{hypotenuse}}\\ \\ : \implies cos\:60\degree = \frac{distance\:between\:wall\:and\:foot\:of\:ladder}{length\:of\:ladder} \\ \\ : \implies \frac{1}{2}= \frac{5}{H} \\ \\ : \implies \frac{H}{2}=5 \\ \\ : \implies H = 5\times 2 \\ \\ \green{: \implies \text{H = 10\: m}}$