oN A LEVEL GROUND, A 5FT. PERSON AND A FLAGPOLE CAST SHADOWS OF 10 FEET AND 60 FEET RESPECTIVELY. WHAT IS THE HEIGHT OF THE FLAGPOLE?

No need for trig, just use a simple ratio ...

height/60 = 5/10
height = 60(1/2) = 30 ft

(did you notice the height of the man is 1/2 of his shadow, then the height of the pole must be 1/2 its shadow, or 1/2 of 60, which is 30 )

To find the height of the flagpole, you can use the concept of similar triangles. Let's denote the height of the flagpole as 'x'.

We have two similar triangles: one formed by the person's height, their shadow, and the ground, and another formed by the flagpole's height, its shadow, and the ground.

The ratio of the person's height to their shadow length is the same as the ratio of the flagpole's height to its shadow length. In other words, since the person's height is 5ft and their shadow is 10ft, we can write:

5ft / 10ft = x / 60ft

To solve for 'x', we can cross-multiply and solve the equation:

10ft * x = 5ft * 60ft
10x = 300ft
x = 30ft

Therefore, the height of the flagpole is 30 feet.