Question

The angle of elevation to the top of the radio atenna on the top of a building is 53.4 degrees. After moving 200 feet closer to the building, the angle of elevation is 63.4 degrees. Find the height of the building if the height of the atenna is 189 feet. Please HELP!

Answer 1

is the height of the antennea AT 189 ft? or is the antennea 189FT tall?

Answer 2

imaging right triangle, where is the h (hight of the building) is one side of the triangle + 189 ft for antenna
now if alpha= angle 53.4 and beta= angles 63.4
on a bottom (other side of the right triangle) - length x will become (x-200) after it's moved
so, tan alpha = (h+189)/x
tan beta=(h+189)/(x-200)
you know angles; you have a system of two ew with two variables - should be able to solve it.
let me know if there is a problem

Answer 3

Actually the height of the antenna is 180ft. Sorry, my mistake!

Answer 4

just input 180 instead of 189 in the above. should work the same

Answer 5

..... antennea = 180?

...... or top of antennea is at 180' ?

Answer 6

Oh and the antenna is 180ft tall.

Answer 7

the antennea is bigger than a football field at the moment

Answer 8

Haha.

Answer 9

tan(53.4) = (180+h)/(200+d)

tan(63.4) = (180+h)/(d)

Answer 10

d = (180+h)/tan(63.4)

tan(53.4) = (180+h)/(200+[(180+h)/tan(63.4)])

tan(53.4.) = (180+h)/[(tan(63.4)180 + 180 + h)/tan(63.4)]

Answer 11

lets clean this up with a = tan(53.4) and b=tan(63.4)

a = (180+h)/[(200b + 180 + h)/b]

180b + hb
a = ---------------
200b + 180 + h

Answer 12

... see if iniks way works better lol

Answer 13

1.3465 = (180+h)/(200+[(180+h)/1.9969)

1.3465 = (180+h)/[(579.392+h)/1.9969])

2.69
---------- = 180 + h
579.392 +h

2.69 = (180 +h) (579.392 +h)

2.69 = h^2 +759.392h +104290.56

...... this is messy :)

Answer 14

Thank you SO much!