If John stands near a 30 foot tall tree and leans a 50 foot tall ladder against the tree that reaches to the top of tree, then how far is John standing away from the tree? (Round to the nearest hundredth)

think 3-4-5 right triangle.

or, do the math:

√(50^2 - 30^2)

yea its right angle triangle with 30 foot being adjacent side and 50 foot hypotenuse

you have to find base using formula
sq.(50^2-30^2)

To find the distance that John is standing away from the tree, we can make use of the Pythagorean Theorem. According to the theorem, in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this scenario, the ladder is the hypotenuse, and the distance that John is standing away from the tree is one of the other sides. The height of the tree is the second side.

Let's denote the distance that John is standing away from the tree as 'x'. We can set up the following equation based on the Pythagorean Theorem:

x^2 + 30^2 = 50^2

Now, we can solve for 'x':

x^2 + 900 = 2500

Subtracting 900 from both sides:

x^2 = 1600

Taking the square root of both sides:

x = √1600

x = 40

Therefore, John is standing approximately 40 feet away from the tree.