Question

The angle of elevation to the top of a building from the foot of the lower is 30° and the angle of elevation to the top of the tower from the foot of the building is 45 degree if the tower is 30 m i find the height of the building

Answer 1

thankyou plz mark me as brainliest

Answer 2

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

$\green{\therefore{\text{Height\:of\:building=17.32\:m}}}$

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

• In the given question information given about

the angle of elevation to the top of a building from the foot of the lower is 30° and the angle of elevation to the top of the tower from the foot of the building is 45 degree if the tower is 30 m.

• We have to Find the height of building.

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

• According to given question :

$\text{Let\:Height\:of\:building\:be\:x}\\\\ \bold{In \: \triangle \: ABC} \\ : \implies tan\:\theta=\frac{\text{perpendicular}}{\text{base}}\\ \\ : \implies tan\:45^{\circ} = \frac{AB}{BC} \\ \\ : \implies 1=\frac{30}{BC}\\ \\ : \implies BC=30\:m\\ \\ \bold{In\:\triangle\:DCB}\\ :\implies tan\:\theta=\frac{p}{b} \\\\ :\implies tan\:30^{\circ}=\frac{DC}{BC}\\\\ :\implies \frac{1}{\sqrt{3}}=\frac{DC}{30}\\\\ \green{:\implies DC=\frac{30\sqrt{3}}{3}}\\\\ \green{\therefore \text{height \: of \: building =17.32\:m}}$