(a) A bus is on opposite side of the road of a building. The distance between the foot of the building and the bus is 20 m. The angle of depression to the bus as observed from the top of the building is 45°. Find the height of the building
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Step-by-step explanation:
Let △ABC be a right angled triangle where ∠B=90
0
and ∠DAC=45
0
as shown in the above figure.
Let x be the distance of object from the building.
Since AD∣∣BC, therefore,
∠DAC=∠BCA=45
0
(Alternate angles)
We know that tanθ=
Adjacentside
Oppositeside
=
BC
AB
Here, θ=45
0
, BC=x m and AB=50
3
m, therefore,
tanθ=
BC
AB
⇒tan45
0
=
x
50
3
⇒1=
x
50
3
(∵tan45
0
=1)
⇒x=50
3
Hence, the distance of the object from the building is 50
3
m.
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