A 9 foot ladder is leaning on a tree. The bottom of the ladder on the ground at a distance of 4 ft from the base of the tree. The base of the tree and the ground for a right angle. What is the distance

The height of the tree is √65 or 8.06 feet

Step-by-step explanation:

Let's use the Pythagorean theorem to find out the height of the tree, this way:

Hypotenuse = length of the ladder = 9 feet

Leg 1 = Distance from the base of the tree to bottom of the ladder = 4 feet

Leg 2 = Height of the tree

Now, replacing with the real values we have:

Leg 2 ² = Hypotenuse² - Leg 1²

Leg 2² = 9² - 4²

Leg 2² = 81 - 16

Leg 2² = 65

√Leg 2² = √65

Leg 2 = √65 or 8.06 feet

The height of the tree is √65 or 8.06 feet