Question

a tree that is 10 feet tall casts a shadow that is 8 feet long. what is the distance from the top of the tree to the tip of the shadow? round to the nearest tenth. 9.4 feet 12.8 feet 3.2 feet 2.8 feet

Explanation:

Step1: Apply Pythagorean theorem

The height of the tree \(h = 10\) feet and the length of the shadow \(s=8\) feet. Let the distance from the top of the tree to the tip of the shadow be \(d\). By the Pythagorean theorem \(d=\sqrt{h^{2}+s^{2}}\).

Step2: Substitute values

Substitute \(h = 10\) and \(s = 8\) into the formula: \(d=\sqrt{10^{2}+8^{2}}=\sqrt{100 + 64}=\sqrt{164}\).

Step3: Calculate the square - root

\(\sqrt{164}\approx12.8\) (using a calculator, \(\sqrt{164}\approx12.8062\) and rounding to the nearest tenth).

Answer:

12.8 feet