Question

at noon, a tree casts a shadow that is 40 feet long. the distance from the top of the tree to the furthest tip of the shadow is 60 feet. not drawn to scale what is the height of the tree? round to the nearest hundredth. 10.00 feet 20.00 feet 44.72 feet 72.11 feet

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse of a right - triangle and \(a\) and \(b\) are the other two sides. In this case, let the height of the tree be \(h\), the length of the shadow \(a = 40\) feet and the distance from the top of the tree to the furthest tip of the shadow \(c=60\) feet. So the formula becomes \(h^{2}+40^{2}=60^{2}\).

Step2: Solve for \(h^{2}\)

Rearrange the formula: \(h^{2}=60^{2}-40^{2}\). Calculate \(60^{2}=3600\) and \(40^{2}=1600\). Then \(h^{2}=3600 - 1600=2000\).

Step3: Solve for \(h\)

Take the square root of both sides: \(h=\sqrt{2000}\approx44.72\) (rounded to the nearest hundredth).

Answer:

44.72 feet