Question

the angle of depression from the top of a building to the foot of the tower is 30 degree and the angle of depression from the top of the tower to the foot of the building is 45degree if the tower is 30m high find the height of the building​

Answer 1

Answer:

the height of building is 17.3m

Answer 2

The height of building=$10\sqrt 3$m

Step-by-step explanation:

In triangle ABC

$\theta=45^{\circ}$

AB=30 m

$tan\theta=\frac{perpendicular\;side}{Base}$

Using the formula

$tan45=\frac{AB}{BC}=\frac{30}{BC}$

$1=\frac{30}{BC}$

Using $tan45^{\circ}=1$

$BC=30 m$

In triangle DBC

$tan30=\frac{DC}{BC}$

$\frac{1}{\sqrt 3}=\frac{DC}{30}$

$DC=\frac{30}{\sqrt 3}\times \frac{\sqrt 3}{\sqrt3 }=10\sqrt 3m$

Hence, the height of building=$10\sqrt 3$m

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