Question

When the sun's angle of elevation is 30 degree the shadow of a post is 6 ft longer than when the angle is 45
degree. find the height of the post

Answer 1

let the height of the post be h ft, let the length of the shadow be x
when angle is 45°, the height of the post and its shadow would be equal, so x = h at 45°

at 30°, length of shadow = h+6

tan 30 = h/(h+6)
1/√3 = h/(h+6)
√3h = h + 6
√3h - h = 6
h(√3 - 1) = 6
h = 6/(√3 - 1) = appr. 8.2 ft
√3h - h =