Question

The angle of elevation of the top of the building form of foot of the tower is 30 degree and the angle of elevation of the top of the tower from the foot of the building is 45 degree if the tower is 30 M height find the height of the building

Answer 1

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

$\green{\therefore{\text{Height\:of\:building=}\frac{30}{\sqrt{3}}\:m}}$

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

• In the given question information given about the angle of elevation of the top of the building form of foot of the tower is 30 degree and the angle of elevation of the top of the tower from the foot of the building is 45 degree if the tower is 30 m height.

• We have to Find the height of building.

$\green{\underline \bold{Given :}} \\ : \implies \text{Angle of elevation of top of a tower from the foot of the building= }45^{\circ} \\ \\ : \implies \text{Angle of elevation of the top of the building to foot of tower =} 30^{\circ} \\\\ :\implies \text{Height of tower= 30 m}\\ \\ \red{\underline \bold{To \: Find:}} \\ : \implies \text{Height\:of\:building(DC)= ?}$

• According to given question :

$\text{Let\:Height\:of\:building\:be\:x}\\\\ \bold{In \: \triangle \: ABC} \\ : \implies tan\:\theta=\frac{\text{perpendicular}}{\text{base}}\\ \\ : \implies tan\:45^{\circ} = \frac{AB}{BC} \\ \\ : \implies 1=\frac{30}{BC}\\ \\ : \implies BC=30\:m\\ \\ \bold{In\:\triangle\:DCB}\\ :\implies tan\:\theta=\frac{p}{b} \\\\ :\implies tan\:30^{\circ}=\frac{DC}{BC}\\\\ :\implies \frac{1}{\sqrt{3}}=\frac{DC}{30}\\\\ \green{:\implies DC=\frac{30}{\sqrt{3}}}\\\\ \green{\therefore \text{height \: of \:building =}\frac{30}{\sqrt{3}}\:m}$