Answer:
12.21 m to the nearest hundredth.
Step-by-step explanation:
Let x m be the height of the tower.
Let y m be the distance from the closest person (B) from the tower.
Then we have the system:
tan 55 = x/y
tan 40 = x / (y + 6) (as line AB = 6)
From the first equation:
x = y tan 55
Substituting in the second equation:
tan 40 = (y tan 55) / (y + 6)
tan 40(y + 6) = y tan 55
y tan 40 + 6 tan 40 = y tan 55
y(tan 40 - tan 55) = - 6 tan 40
y = -6 tan 40 / (tan 40 - tan 55)
y = 8,547 m
From the first equation
tan 55 = x / 8.547
x = 8.547 tan 55
= 21.21. m
