Question

a florist makes a string of flowers along a pole and ties it at a point 20 feet high on the wall and to the floor 8 feet away from the wall. he then changes his mind and moves the flowers down the wall 10 feet. approximately how far away from the wall would he now have to tie the flowers on the floor? a 15.4 ft

Explanation:

Step1: Calculate the original length of the string

The original situation forms a right - triangle with height $h_1 = 20$ feet and base $b_1=8$ feet. Using the Pythagorean theorem $c=\sqrt{a^{2}+b^{2}}$, the length of the string $L$ (the hypotenuse of the right - triangle) is $L=\sqrt{20^{2}+8^{2}}=\sqrt{400 + 64}=\sqrt{464}$.

Step2: Calculate the new height and use the Pythagorean theorem again

After moving the flowers down 10 feet, the new height $h_2=20 - 10=10$ feet. Let the new base be $b_2$. Since the length of the string remains the same, we have $L=\sqrt{10^{2}+b_2^{2}}$. But we know $L = \sqrt{464}$, so $\sqrt{464}=\sqrt{10^{2}+b_2^{2}}$. Squaring both sides gives $464=100 + b_2^{2}$. Then $b_2^{2}=464 - 100=364$, and $b_2=\sqrt{364}\approx19.1$ feet.

Answer:

Approximately 19.1 feet