John bought a ramp $15$ ft long he bought a ramp thats $15$ ft long his deck is $5$ tt long he wants to know how many feet the ramp would be off the ground if the ramp was attached to the deck

Full solution

Q. John bought a ramp

15

ft long he bought a ramp thats

15

ft long his deck is

5

tt long he wants to know how many feet the ramp would be off the ground if the ramp was attached to the deck

Question Prompt: question_prompt: How many feet off the ground will the ramp be if it's attached to the deck?
Pythagorean Theorem: Since the ramp is $15 \, \text{ft}$ long and the deck is $5 \, \text{ft}$ long, we can use the Pythagorean theorem to find the height of the ramp off the ground. The ramp forms the hypotenuse of a right triangle, and the deck forms one of the legs.
Calculation: The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse ( $c$ ) is equal to the sum of the squares of the lengths of the other two sides ( $a$ and $b$ ). So, $c^2 = a^2 + b^2$ .
Subtraction: We know the length of the ramp (hypotenuse, $c$ ) is $15$ ft and the length of the deck (one leg, $a$ ) is $5$ ft. We need to find the height of the ramp off the ground (other leg, $b$ ). So, we have $15^2 = 5^2 + b^2$ .
Solve for $b^2$ : Calculating the squares, we get $225 = 25 + b^2$ .
Square Root Calculation: Subtract $25$ from both sides to solve for $b^2$ , we get $b^2 = 225 - 25$ .
Final Answer: Now, $b^2 = 200$ .
Final Answer: Now, $b^2 = 200$ . To find $b$ , we take the square root of both sides. So, $b = \sqrt{200}$ .
Final Answer: Now, $b^2 = 200$ . To find $b$ , we take the square root of both sides. So, $b = \sqrt{200}$ . Calculating the square root, we get $b \approx 14.14$ ft.