Question

The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 6.5 metre from the wall find the length of the ladder

Answer 1

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Answer 2

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

$\green{\therefore{\text{Length\:of\:ladder=13\:m}}}$

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

• In the given question information given about the angle of elevation of a ladder leaning against a wall is 60º and the foot of the ladder is 6.5 m away from the wall.

• We have to find the length of ladder.

$\green{\underline \bold{Given :}} \\ : \implies \text{Distance\:between\:wall\:and\:foot\:of\: ladder=6.5\: m} \\ \\ : \implies \text{Angle\:of\:elevation=}60^{\circ}\\\\ \red{\underline \bold{To \: Find:}} \\ : \implies \text{Length\:of\:ladder= ?}$

• Accroding to given question :

$\bold{In \: \triangle \: ABC} \\ : \implies cos \: \theta = \frac{\text{Base}}{\text{Hypotenuse}} \\ \\ : \implies cos\: 60^{\circ}= \frac{BC}{AC} \\ \\ : \implies \frac{1}{2}= \frac{6.5}{AC} \\ \\ : \implies AC= 6.5\times 2 \ \\ \\ \green{ : \implies \text{AC=13\:m}}$