Final answer:
The height of Sam's ramp is found by using the Pythagorean theorem. With the base of the ramp as one leg and the ramp length as the hypotenuse, the height of the ramp, being the other leg, is calculated to be 16 inches.
Step-by-step explanation:
The student is looking to find the height of a ramp where the base of the ramp is 30 inches and the length of the ramp is 34 inches. To solve this problem, we need to use the Pythagorean theorem which states that in a right triangle, the sum of the squares of the two legs (a and b) is equal to the square of the hypotenuse (c).
In this case, the base of the ramp forms one leg (a = 30 inches), the height of the ramp would be the other leg (b), and the length of the ramp is the hypotenuse (c = 34 inches).
The theorem can be expressed as a2 + b2 = c2. Plugging the known measurements into the equation: 302 + b2 = 342, gives us 900 + b2 = 1156. Subtracting 900 from both sides we get b2 = 256 and taking the square root of both sides we find that b = 16 inches. So, the height of the ramp is 16 inches.