Question

The angle of elevation of a 5m long ladder leaning against a wall is 45 degree and the foot of the ladder is 3m away from the wall. the height of wall up to the point where the ladder is resting against it is.

Answer 1

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

$\green{\therefore{\text{Height\:of\:wall=}2.5\sqrt{2}\:m}}$

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

• In the given question information given about the angle of elevation of a 5m long ladder leaning against a wall is 45 degree and the foot of the ladder is 3m away from the wall.

• Wh have to find the height of wall up to the point where the ladder is resting against it is.

$\green{\underline \bold{Given :}} \\ : \implies \text{Length\:of\: ladder= 5\: m} \\ \\ : \implies \text{Angle\:of\:elevation= }45^{\circ}\:m\\\\ :\implies \text{Distance\:between\:wall\:and\:foot\:of\:ladder =3\:m}\\ \\ \red{\underline \bold{To \: Find:}} \\ : \implies \text{Height\:of\:wall= ?}$

• Accroding to given question :

$\bold{in \: \triangle \: ABC} \\ : \implies sin \: \theta = \frac{\text{Perpendicular}}{\text{Hypotenuse}} \\ \\ : \implies sin \: 45 ^ { \circ} = \frac{AB}{AC} \\ \\ : \implies \frac{1}{ \sqrt{2} } = \frac{AB}{5} \\ \\ : \implies AB = \frac{5}{ \sqrt{2} } \\ \\ : \implies AB = \frac{5 \sqrt{2} }{2} \\ \\ \green{ : \implies \text{AB = 2.5 }\sqrt{2} \: m}$