Answer:
a) 125.865 ft
b) 321.676 ft
c) 195.811 ft
Step-by-step explanation:
Given:-
- The height of the building, H = 150 ft
- The angle of elevation ( friend - top of building ), θ1 = 50°
- The angle of elevation ( zombie - top of building ), θ2 = 25°
Find:-
a) How far away is your friend from the building
b) How far away is the zombie from the building
c) How far away is the zombie from your friend
Solution:-
- We will consider the two right angle triangles with similar height ( H ) which denotes the height of the building.
- The distance your friend is from the building is ( x1 ) and looks up to the top of the building with angle of elevation of ( θ1 ).
- We can apply the trigonometric ratio for the right angle triangle formed between your friend, foot of the building and you ( on top of the building ):
tan ( θ1 ) = H / x1
x1 = H / tan ( θ1 )
x1 = 150 / tan ( 50° )
x1 = 125.865 ft ... Answer ( a )
- The distance zombie is from the building is ( x2 ) and looks up to the top of the building with angle of elevation of ( θ2 ).
- Similarly, apply the appropriate trigonometric ratio for the right angle triangle formed between zombie, foot of the building and you ( on top of the building ):
tan ( θ2 ) = H / x2
x2 = H / tan ( θ2 )
x2 = 150 / tan ( 25° )
x2 = 321.676 ft ... Answer ( b )
- The distance between your friend and the zombie ( s ) can now be determined from subtracting the distance of your friend from the building from distance of the zombie from the building:
s = x2 - x1
s = 321.676 - 125.865
s = 195.811 ft ... Answer ( c )
