CBSE Class 10 Answered
Good to know that your exam went off well.
Here's the solution to your question.
Assume AB to be the 8m tall building.with A as its top and B as its bottom.
Let EC be the multistoreyed building with E as its top and C as its bottom.
Mark D on EC such that DC=8 m(so ABCD is a rectangle)
Let BC=AD= x m and ED = h m
According to question,
angle EAD=30(alternate angle of the angle of depression)
and
angle EBC=45(same reason as above)
In triangle EAD,
tan 30=ED/AD=h/x
So,
x=hcot30..(i)
Next,
in triangle EBC,
tan45=(h+8)/x
So,
x=h+8..(ii)
Equating the value of x from both equations, we get,
h+8=h cot 30
h+8=h*(1.732)
8=h*(0.732)
h=8/0.732
calculate the final step and you will have the answer of h.
Add 8 to it and you will get the height of the multistoreyed building.