Question

The length of a ladder leaning against a wall is twice the distance between the foot of the ladder and the wall.find the angle made by the ladder with ground?​

Answer 1

angle made by the ladder with ground = 60°

Step-by-step explanation:

The length of a ladder leaning against a wall is twice the distance between the foot of the ladder

Let say Distance between foot of the Ladder and Wall =  D

Length of Ladder  = 2 D

Angle made by Ladder with wall = α

Cosα  =  Base / Hypotenuse

=> Cosα  = Distance between foot of the Ladder and Wall / Length of Ladder

=> Cosα  = D/2D

=> Cosα  = 1/2

=> Cosα  = Cos60°

=> α  = 60°

angle made by the ladder with ground = 60°

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Answer 2

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

$\green{\therefore{\text{Angle\:made\:by\:ladder\:with\:ground=60\degree}}}$

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

• In the given question information given the length of a ladder leaning against a wall is twice the distance between the foot of the ladder and the wall.

• We have to find the angle made by the ladder with ground.

$\green{\underline \bold{Given :}} \\ : \implies \text{Length\:of\: ladder=2\:times\:Distance\:between\:wall\:and\:foot\:of\:ladder} \\ \\ \red{\underline \bold{To \: Find:}} \\ : \implies \text{Angle\:made\:by\:ladder\:with\:ground= ?}$

• Accroding to given question :

$\text{Let\:distance\:between\:wall\:and\:foot\:of\:ladder=x}\\\\\text{Length\:of\:ladder=2x} \\\\\bold{In \: \triangle \: ABC} \\ : \implies cos\:\theta=\frac{\text{Base}}{\text{hypotenuse}}\\ \\ : \implies cos\:\theta = \frac{distance\:between\:wall\:and\:foot\:of\:ladder}{length\:of\:ladder} \\ \\ : \implies cos\:\theta= \frac{x}{2x} \\ \\ : \implies cos\:\theta=\frac{1}{2} \\ \\ : \implies cos\:\theta = cos\:60\degree \\ \\ \green{: \implies \theta = 60\degree}$