two points A and B 80 ft. apart lie on the same side of a tower and in a horizontal line through its foot. if the angle of elevation of the top of the tower at A is 21 degree and B is 46 degree, find the height of the tower.

Answer 1

Let P be the foot of the tower, and h be the height of the tower
let AP = x , then BP = 80-x
I see two right-angled triangles

tan21 = h/x ---> h = xtan21
tan46 = h/(80-x) --> h = (80-x)tan46

xtan21 = (80-x)tan46
xtan21 = 80tan46 - xtan46
xtan21 + xtan46 = 80tan46
x(tan21 + tan46) = 80tan46
x = 80tan46/(tan21 + tan46) ----- I have not yet touched a calculator

you do the button pushing to get x
then plug x into
h = xtan21

Answer 2

Two points A and B 80 ft apart lie on the same side of a tower
and in a horizontal line through its foot. If the angle of
elevation of the top of the tower at A is 21o and at B is 46o,
find the height of the tower