Question

the bottom of the ladder must be placed 6 feet from a deck the latter is 10 feet long how far above the ground does the ladder touch the deck

Answer 1

The ladder touches the deck at 8 feet high.

Given:
distance of the bottom of the ladder from the deck: 6 feet
length of the ladder: 10 feet

Find the height where the top of the ladder touches the deck.

We can visual that a right angle triangle is formed between the ladder, the deck, and the ground.

The length of the ladder is the hypotenuse. The length from the deck to the bottom of the ladder is the measurement of one side.

Using the Pythagorean theorem: a² + b² = c² ; we can find the measurement of the other side.
a = 6 ft ; b = unknown ; c = 10 ft

6² + b² = 10²
b² = 10² - 6²
b² = 100 - 36
b² = 64
b = √64
b = 8 feet.