Two buildings A and B are 100m apart from each other and their angel of evelvation from the top of the building A to the top of building B is 20dgree .The angle of elevation from the base of building B to the top of building A is 50Dgree. Find the hight of building B?
Answers
Answer:
Step-by-step explanation:
Let x be the total height of the cliff. Therefore, the height of the cliff above the building is (x−24) and let y be the distance from the base of the building to the base of the cliff.
From the above adjoining figure, DE=BC=y.
We know that tanθ= Oppositeside/Adjecent side = AB/BC
In △ABC, ∠B=90 degree and ∠C=60 degree
Here, θ=60 degree , BC=y m and AB=x m, therefore,
tanθ=
BC
AB
⇒tan60
0
=
y
x
⇒
3
=
y
x
(∵tan60
0
=
3
)
⇒x=
3
y...........(1)
Also, in △AED, ∠E=90
0
and ∠D=45
0
.
Here, θ=45
0
, AE=(x−24) m and EC=y m, therefore,
tanθ=
EC
AE
⇒tan45
0
=
y
x
⇒1=
y
x−24
(∵tan45
0
=1)
⇒y=x−24...........(2)
Substitute the value of equation 1 in equation 2, we get
y=
3
y−24
⇒y−
3
y=24
⇒y(
3
−1)=24
⇒y=
3
−1
24
Now, substitute the value of y in equation 1:
x=
3
(
3
−1
24
)
⇒x=
3
−1
24
3
Hence, the height of the cliff is
3
−1
24
3
m.