Question

the sun is shining down on a tree, making a shadow that measures 12 feet tall from the trees base. if the distance between the end of the shadow and the top of the tree is 20 feet, how tall is the tree? select one of four 18 ft. 10 ft. 16 ft. 14 ft. remaining attempts: 1

Explanation:

Step1: Apply Pythagorean theorem

Let the height of the tree be \(h\). The shadow length \(a = 12\) feet and the hypotenuse \(c=20\) feet. According to the Pythagorean theorem \(a^{2}+h^{2}=c^{2}\), so \(h^{2}=c^{2}-a^{2}\).

Step2: Substitute values

Substitute \(a = 12\) and \(c = 20\) into the formula: \(h^{2}=20^{2}-12^{2}\).
Calculate \(20^{2}=400\) and \(12^{2}=144\). Then \(h^{2}=400 - 144=256\).

Step3: Solve for \(h\)

Take the square root of \(h^{2}\), \(h=\sqrt{256}\). Since \(h>0\), \(h = 16\).

Answer:

16 ft.