The distance between point on the ground from the top of the building is 396 meter, if the building is 280 m high and The angle of depression from the top of a building to a point on the ground is 45 degrees.
Step-by-step explanation:
The given is,
The angle of depression from the top of a building to a point on the ground is 45 degrees.
Height of the building is 280 meter.
Step: 1
Given diagram is a right angled diagram,
For right angle triangle,
90° = 45° + 45°
= 90°
Trignometric ratio,
sin ∅ = [tex]\frac{Opp}{Hyp}[/tex]....................(1)
For the above ratio take the bottom angle, that is angle of depression from the top of a building to a point on the ground is 45 degrees.
Where, Opp side = 280 meters
Hyp side = x
∅ = 45°
Equation (1) becomes,
sin 45° = [tex]\frac{280}{x}[/tex]
0.70710678 = [tex]\frac{280}{x}[/tex]
x = [tex]\frac{280}{0.70710678}[/tex]
x = 395.979
Distance between point on the ground from the top of the building, x ≅ 396 meter
Trignometric ratio,
cos ∅ = [tex]\frac{Adj}{Hyp}[/tex]
Cos 45 = [tex]\frac{Adj}{396}[/tex]
Adj = (0.70710678)(396)
Bottom length, Adj = 280 meter
Result:
The distance between point on the ground from the top of the building is 396 meter.
