Two observation towers A and B are located 300 ft apart as s

Two observation towers A and B are located 300 ft apart, as shown. An object on the ground between the towers is observed at point C, and the observer on tower A notes that the angle CAB is 68degree 10\'. At the same time, the observer on tower B notes that the angle CBA is 72degree 30\'. Assuming a horizontal surface and towers of equal height, how far is the object from each tower and how high are the towers?

Solution

68deg10\' ---> 68.17 deg ; 72deg 30\' ---> 72.5

Let object C is at x distance from Tower A and ( 300-x) from Tower B

Let heights of tower be y

Applying tan formula : tan 68.17 = y/x ----(1)

tan72.5 = y/( 300-x)   ---(2)

Divide equation 2 by equ 1:

tan72.5 / tan68.17 = (300-x)/x

1.27 =(300-x)/x

1.27x = 300-x

x= 132.16 ft from Tower A

and 300 -132.16 = 167.84 ft from Tower B

Height of tower y = 132.16*tan68.17 = 329.92 ft