Answer:
95.82 ft
Step-by-step explanation:
Since they are in line with the obelisk and are 25 feet apart,
they can be sketched to represent a right angle triangle, the points representing A and B, let the height of the obelisk be h, the distance between the foot of the obelisk and B = x ft so that the distance between the foot of the obelisk and A = x ft + 25 ft.
Using trigonometrical ratio
tan 54 = [tex]\frac{h}{x+25ft}[/tex]
tan 65 = [tex]\frac{h}{x}[/tex]
make x subject of the formula
x = [tex]\frac{h}{tan 65}[/tex] = 0.466 h
substitute for x in the first equation
1.376 ( x + 25 ft) = h
1.376 ( 0.466 h + 25 ft) = h
0.641 h + 34.4 = h
34.4 ft = h - 0.641 h
34.4 ft = 0.359 h
h = 34.4 ft / 0.359 = 95.82 ft
