SOLUTION: a person standing at point A notices that the angle of elevation to the top of the antenna is 48° 30'. A second person standing 35.0 feet farther from the antenna than the person

Algebra ->  Triangles -> SOLUTION: a person standing at point A notices that the angle of elevation to the top of the antenna is 48° 30'. A second person standing 35.0 feet farther from the antenna than the person       Log On


   

Question 1145693: a person standing at point A notices that the angle of elevation to the top of the antenna is 48° 30'. A second person standing 35.0 feet farther from the antenna than the person at A finds the angle of elevation to the top of the antenna to be 41° 10'. How far is the person at A from the base of the antenna?
(Round your answer to the nearest whole number.)
________ft
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
a person standing at point A notices that the angle of elevation to the top of the antenna is 48° 30'.
A second person standing 35.0 feet farther from the antenna than the person at A finds the angle of elevation to the top of the antenna to be 41° 10'.
How far is the person at A from the base of the antenna?
:
let x = the distance from A to the base of the antenna
let h = the vertical height of the antenna
:
Change 48 30' to 48.5 degrees, change 41 10' to 41.167 degrees
Use the tangent of these two angles
tan(48.5) = h%2Fx
tan(48.5)x = h
and
tan(41.167) = h%2F%28%28x%2B35%29%29
tan(41.167)(x+35) = h
h = h therefore
tan(48.5)x = tan(41.167)(x+35)
find the actual tangent of these two angles
1.1303x = .8744(x+35)
1.1303x = .8744x + 30.6
1.1303x - .8744x = 30.6
.2559x = 30.6
x = 30.6%2F.2559
x = 119.58, 120 ft from A to the base of the Antenna
:
:
you can confirm this, find the height of the antenna using both positions
tan(48.5)*120 = 135.6 ft
tan(41.167)*155 = 135.5 ft, close enough