Question 169890
You can use the principle of similar triangles to solve this problem.
"Corresponding sides of similar triangles are proportional"
Imagine the man (m) as representing the height of a right triangle while his shadow (b) represents the base of this triangle.
Similarly, the height of the flagpole (h) represents the height of a similar right triangle while the shadow (s) represents the base of this triangle.
You can form a proportion to represent the situation given in the problem:
"The height of the man is proportional to the height of the flagpole as the length of the man's shadow is to the length of the flagpole's shadow."
{{{m/b = h/s}}} Substitute the given numbers: m = 6ft., s = 7.8ft., h = the height of the flagpole (to be determined), and s = 195ft.
{{{6/7.8 = h/195}}} Multiply both sides by 195.
{{{6(195)/7.8 = h}}} so...
{{{h = 150}}}feet.  This is the height of the flagpole.