Question

can someone check me? Medal award!

Two sightings are taken of a tv tower. The first gives an elevation of 23 degrees. The second sighting is taken 400 ft farther from the tower and gives an elevation of 20.5 degrees. How tall is the tower?

Answer 1

I did tan23(x)=tan20.5(x+400)

.4244748162x=.3738846795x+149.5538718

I get x=2956.186355

Answer 2

23 is the 1st angle
x is the adjacent
h is the opposite or the height

so tan 23 = h/x -> eqn 1


x + 400 will be the adjacent
20.5 angle of the 2nd
you are looking for the opposite or the height..

so tan 20.5 = h/(x+400)->eqn 2

rearrange the eqns in terms of h
eqn1: h = x tan 23
eqn2: h= (x+400)(tan 20.5)

Combine those two equations together

x(tan 23) = (x+400)(tan 20.5)

solve for x:
x(tan 23) = x(tan 20.5)+ 400(tan 20.5)
x(tan 23 - tan 20.5) = 400 (tan 20.5)
x= 400 (tan 20.5)/(tan 23 - tan 20.5)

x = 2956.18 yes, it seems like we got the same answer

BUT, this isn't the height of the tower yet.
This is the distance between the 1st and the tower.
To calculate for h (height) substitute the value of x in any of those equation I posted above.

Answer 3

thanks so much I got 1254.82666