Question

During a​ hurricane, thousands of pine trees snapped off to form right triangles. Suppose that for one such​ tree, the vertical distance from the base of the broken tree to the point of the break was 4.2 ft. The length of the broken part was 12.1 ft. How far along the ground was it from the base of the tree to the point where the broken part touched the​ ground? It is approximately ___ ft or ft^2 from the base of the tree to the point where the broken part touches the ground.

​(Type an integer or decimal rounded to the nearest tenth as​ needed.)

Answer 1

Using the Pythagorean theorem:

a^2 + c^2 = c^2

Where a and b are the base and height and c is the hypotenuse.

You are given the height and the hypotenuse:

4.2^2 + b^2 = 12.1^2

17.64 + b^2 = 146.41

Subtract 17.64 from both sides:

b^2 = 128.77

Take the square root of both sides:

b = 11.347 feet

b = 11.3 feet.