When the angle of elevation of the sun is 30, the shadow of a vertical yower is 20m longer than when the elevation of the sun is 60.find the height of the tower
Make 2 sketches, one for the 30° angle triangle, another for the 60° triangle
let the height be h m (the height would not change)
let the length of the shadow for the 60° angle be x m, then the length
of the shadow for the 30° would be x+20
tan60 = h/x ---> h = xtan60
tan30 = h/(x+20) ---> h = (x+20)tan30
(x+20)tan30 = xtan60
xtan60 - xtan30 = 20tan30
x(tan60-tan30) = 20tan30
x= ....
once you have x, then in h = xtan60 is your result