The shadow cast by a television tower is 171 ft 10 in. A pole that is stuck in the ground nearby has 2 ft sticking above the ground and casts a shadow that is 6 ft 3 in. in length. Based on this information, how high is the television tower?

the height is 54.99 ft or 659.84 in

Step-by-step explanation:

We know that the sides of similar triangles are proportional, so we can write:

2 ft / 6 ft 3 in = x / 171 ft 10 in

Now what we must do first and pass everything to the same unit of measurement:

Knowing that 1 foot equals 12 inches:

6 ft 3 in = 6 ft * 12 in / ft + 3 in = 72 + 3 = 75 in

171 ft 10 in = 171 ft * 12 in / ft + 10 in = 2052 + 10 = 2062 in

2 ft = 2 ft * 12 in / ft = 24 in

replacing:

24 in / 75 in = x / 2062 in

x = 24 * 2062/75

x = 659.84 in

Or they would also be 659.84 in * 1 ft / 12 in = 54.99 ft

That is, the height is 54.99 ft or 659.84 in