posted by Lynn on .
A person stands at a distance from the tower and eyes the top of the tower at 30 degree angle of elevation. He then walks 425 feet towards the tower and eyes the top of the tower at a 58 degree angle of elevation. The person is 5 feet tall. How tall is the tower?
solve the problem for a person of height zero, then add 5 feet to the answer. Also assume his eyes are on the top of his head.
If he starts at distance x, and the tower has height h, then
h/x = tan 30
h/(x-425) = tan 58
eliminate x to get
h/tan30 = h/tan58 + 425
now just solve for h.
This is easy problem if you draw the triangles properly.
If we consider the height of the tower above the person to be x and the distance remaining to reach the tower from where he made the last measurement to be y then
tan 32 = y/x
0.625 = y/x
x = y/0.625 = 1.6 y
but we also know from the larger triangle (the starting point) that
tan 30 = x/(425+y)
0.577 = x/(425+y)
x = 245.37 + 0.577 y
substitute from first equation into second one
1.6 y = 245.37 + 0.577 y
1.023 y = 245.37
y = 245.37/1.023= 239.85 feet
x = 1.6 * 239.85 = 383.76 feet
the height of the tower = 5 + 383.76= 388.76 feet
Thank you so much for the help.