Question

PLEASE IS IMPORTANT NEED ANSWER QUICK The sun casts a shadow from a flag pole.The length of the pole is 3 feet longer than the length of the shadow. The distance from the end of the shadow to the top of the pole is three feet longer than the pole

A.Write an equation representing this information

B.Find the height of the pole

Answer 1

Part 1)
`{x^(2) -12x=0`

Part 2) The height of the pole is
`12\ ft`

Explanation:

Let

x------> the length of the pole

y------> the length of the shadow

we know that

`x=y+3`

`y=x-3` -----> equation A

Applying the Pythagoras Theorem to find the distance (hypotenuse in a right triangle)

`\sqrt{x^(2) +y^(2)}=x+3` -----> equation B

substitute equation A in equation B and solve for x

`\sqrt{x^(2) +(x-3)^(2)}=x+3`

squared both sides

`{x^(2) +(x-3)^(2)}=(x+3)^(2)`

`x^(2) +x^(2)-6x+9=x^(2)+6x+9`

`x^(2) -12x=0` -----> equation that represent the situation

solve for x

`x^(2) =12x`

`x=12\ ft`