Find the height of the post.?

Question

When the sun’s angle of elevation is 30°, the shadow of a post is 6 ft. longer than when the angle is 45°. Find the height of the post.

Answer 1

Let h = height of post
x is length of shadow when angle is 45°
x + 6 is length of shadow when angle is 30°

tan 30° (x + 6) = h
tan 45°( x ) = h

x tan 45° = x tan 30° + 6 tan 30°
x (tan 45° - tan 30°) = 6 tan 30°
x = 8.2
tan 45° = h / 8.2
h = tan 45° (8.2)
h = 8.2 ft

Answer 2

Using SOH-CAH-TOA.
tan(30°) = opposite / adjacent.
tan(30°) = 1 / √3

Let n be the length of the post (opposite), then the length of the shadow (adjacent) will be n * √3

tan(45°) = opposite / adjacent
tan(45°) = 1

At 45°, the post will cast a shadow that is n (same length as the post)

Length of shadow at 30° = length of shadow at 45° + 6 ft.
n*√3 = n + 6

n√3 - n = 6
n(√3 - 1) = 6
n = 6 / (√3 - 1)

n is approximately 8.2 feet high.

Answer 3

let h = height of post
x shadow when sun’s angle of elevation is 30°
h= x tan 45 = (x + 6) tan 30
x tan 45 = x tan 30 + 6 tan 30
x tan 45 - x tan 30 = 6 tan 30
x (tan 45 - tan 30 ) = 3.4641
x = 8.1962
h = x tan 45 = 8.1962 tan 45 = 8.1962

Answer 4

height of the post
= 6ft/(cot30deg -- cot 45deg)
= 6ft/(1.732 -- 1.000)
= 6/0.732 ft
= 8.19 ft answer.

Answer 5

8.2ft