The length of the support post is 40 ft.
Solution:
Given, the height of the wall is 20 ft; support post forms 30 degree
Refer the attached image
Let us name the triangle as ABC where AB is the wall (opposite side) of 20 ft and [tex]\angle A[/tex] is 30 degree ([tex]\theta[/tex]) and AC is the length of the post.
To find: The length of the post (AC)
we know the formula, [tex]sin\theta=\frac{opp}{hyp}[/tex] (trigonometric formula)
On substituting the values we get,
[tex]\Rightarrow sin(30^{\circ})=\frac{20}{AC}[/tex]
The value of sin 30 degree is 0.5
[tex]\Rightarrow 0.5=\frac{20}{AC}\rightarrow AC=\frac{20}{0.5}\rightarrow AC=40 ft[/tex]
