Posted by Lynn on Sunday, January 26, 2014 at 3:37am.
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?

trig  Steve, Sunday, January 26, 2014 at 6:46am
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/(x425) = tan 58
eliminate x to get
h/tan30 = h/tan58 + 425
now just solve for h.

trig  Hussein, Sunday, January 26, 2014 at 6:50am
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

trig  Lynn, Sunday, January 26, 2014 at 11:47am
Thank you so much for the help.
Answer This Question
Related Questions
 Math  If an observer stands at a certain point in the same horizontal plane as ...
 Math  to measure the height of the Eiffel Tower in Paris, a person stands away ...
 Math trig  Two towers 50 meters apart from the top of the shorter tower to the ...
 trig  On an inclined road, which makes an angle of 25 degrees with the ...
 math  A radio tower stands on the top of a hill that is 85 feet high. From the ...
 TRIG Help help help test tommarow  A TV tower stands on top of the Empire State...
 Calculus  The CN Tower is 553 m tall. A person is south of the tower, in a boat...
 Trig  From a point P on level ground, the angle of elevation of the top of a ...
 math  Jack looks at a clock tower from a distance and determines that the angle...
 Trigonometry  A 30foot flagstaff is fixed in the center of a circular tower 40 ...
More Related Questions