Question

two people decide to find the height of an obelisk. they position themselves 25 feet apart in line with, and on the same side of, the obelisk. if they find that the angles of elevation from the ground where they are standing to the top of the obelisk are 65 degrees and 54 degrees, how tall is the obelisk

Answer 1

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 = $\frac{h}{x+25ft}$

tan 65 = $\frac{h}{x}$

make x subject of the formula

x = $\frac{h}{tan 65}$ = 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