Question

The distance from a person to the top of the flag pole is 15 feet. If the flag pole's height is 3 feet longer than the distance of the base to the person, find the length of the flag pole

Answer 1

Length of the flag pole is 12 ft

Explanation:

Based on understanding the problem, it forms a right angle triangle. So, we can use Pythagoras' theorem.

c² = a² + b²

let x = the distance of the pole to the person

x + 3 = the height of the flag pole

15ft is the hypotenuse

15² = x² + (x+3)²

225 = x² + x² + 6x + 9

225 = 2x²+ 6x + 9

rearrange the equation

2x²+ 6x + 9 = 225

2x²+ 6x - 216 = 0

divide both sides by 2

x² + 3x - 108 = 0

by factoring

(x+12)(x-9)=0

x = -12

x = 9

x + 3 = the height of the flag pole

9 + 3 = 12

Answer 2

Answer: 39 feet

Explanation:

Let's use a variable to represent the distance from the base of the flag pole to the person. You can call this distance "x."

According to the information given:

1. The distance from the person to the top of the flag pole is 15 feet.

2. The flag pole's height is 3 feet longer than the distance from the base to the person (which is x).

So, the height of the flag pole (h) can be expressed as:

h = x + 3

Now, we can use the Pythagorean theorem because we have a right triangle formed by the person, the base of the flag pole, and the top of the flag pole. The hypotenuse of this triangle is the height of the flag pole, and the other two sides are the distance from the person to the base (x) and the distance from the person to the top of the flag pole (15 feet).

According to the Pythagorean theorem:

h² = x² + 15²

Now, we can substitute the expression for "h" from the first equation:

(x + 3)² = x² + 15²

Let's solve for "x":

x² + 6x + 9 = x² + 225

Now, subtract x² from both sides of the equation to simplify:

6x + 9 = 225

Subtract 9 from both sides:

6x = 225 - 9

6x = 216

Now, divide by 6 to solve for "x":

x = 216 / 6

x = 36

So, the distance from the base of the flag pole to the person (x) is 36 feet. Now, we can find the height of the flag pole (h):

h = x + 3

h = 36 + 3

h = 39 feet

Therefore, the length of the flag pole is 39 feet.