Final answer:
Using the Pythagorean Theorem, the height of the tallest branch the ladder can reach is calculated to be 15 feet. The bottom of the ladder is 8 feet from the tree and the ladder is 17 feet long.
Step-by-step explanation:
The student is asking a question related to Pythagorean Theorem, which is a part of Mathematics. To find the height of the tallest branch that a 17-foot long ladder can reach when the bottom is placed 8 feet from a tree, we can set up the equation based on the theorem: a^2 + b^2 = c^2, where 'c' is the length of the ladder (hypotenuse), 'a' is the height of the branch (opposite side), and 'b' is the distance from the tree (adjacent side).
Firstly, plug in the known values:
a^2 + 8^2 = 17^2
a^2 + 64 = 289
Subtract 64 from both sides to isolate a^2:
a^2 = 225
Take the square root of both sides to solve for 'a':
a = 15 feet
Hence, the height of the tallest branch that the ladder can reach is 15 feet.