25. The angles of depression of the top and the bottom of a 8 m tall b

1.	25. The angles of depression of the top and the bottom of a 8 m tall building from the top of a multi-storeyed building are 309 and 45°, respectively. Find the height of the multi-storeyed buildingand the distance between the two buildings.
Answer» Angle of depression of top of the8m tall building from the top of thehm multi-story building isθ1=300 and angle of depression of bottom of the8m tall building from the top of thehm multi-story building isθ2=450 Let the difference of their heightx=h−8∴tan30=xdor d=x⋅√3;(1), wheredis the horizontal distance between two buildings. Alsohd=tan45orx+8d=tan45or (x+8)=d;(2)From equation (1) and equation (2) we get x+8=√3⋅xorx(√3−1)=8orx=8√3−1≈10.93m ∴h≈10.93+8=18.93m andd=x+8=18.93m The height of the multi-story building is18.93m and distance between the two buildings is also18.93m [Ans]

25. The angles of depression of the top and the bottom of a 8 m tall building from the top of a multi-storeyed building are 309 and 45°, respectively. Find the height of the multi-storeyed buildingand the distance between the two buildings.

Answer»

Angle of depression of top of the8m tall building

from the top of thehm multi-story building isθ1=300

and angle of depression of bottom of the8m tall building

from the top of thehm multi-story building isθ2=450

Let the difference of their heightx=h−8∴tan30=xdor

d=x⋅√3;(1), wheredis the horizontal distance between

two buildings. Alsohd=tan45orx+8d=tan45or

(x+8)=d;(2)From equation (1) and equation (2) we get

x+8=√3⋅xorx(√3−1)=8orx=8√3−1≈10.93m

∴h≈10.93+8=18.93m andd=x+8=18.93m

The height of the multi-story building is18.93m and

distance between the two buildings is also18.93m [Ans]