Answer:
18.7939 m
Step-by-step explanation:
-Let x be the distance between John and clock tower.
-Let y be the vertical distance from the eyes of the two men standing to the top of the clock tower.
#Taking the right triangle ACD:
[tex]\Tan \ theta=\frac{Perpendicular \ Height}{Base}\\\\Tan \ 60\textdegree=\frac{y+1.5}{x}\\\\y=x \ Tan \ 60\textdegree -1.5[/tex]
#Taking the right triangle ABD:
[tex]\Tan \ theta=\frac{Perpendicular \ Height}{Base}\\\\Tan \ 40\textdegree=\frac{y+1.5}{x+20}\\\\y=(x+20)\ Tan \ 40\textdegree -1.5[/tex]
#We equate the two yo solve for x and y;
[tex](x+20)\ Tan \ 40\textdegree -1.5=x\ Tan \ 60\textdegree -1.5\\\\(x+20)\ Tan \ 40\textdegree=x\ Tan \ 60\textdegree\\\\0.8391x+16.7820=1.7321x\\\\x=18.7939[/tex]
Hence, John's distance from the tower's base is 18.7939 m
