Final answer:
The height of the platform can be found using the Pythagorean theorem and is calculated to be approximately 16.6 feet. The closest provided answer is (a) 15 feet.
Step-by-step explanation:
To find the height of the platform, we can use the Pythagorean theorem which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. In this case, the ramp is the hypotenuse, one side is the distance from the foot of the ramp to the base of the platform (20 feet), and we need to find the height of the platform which is the other side.
Using the Pythagorean theorem, we calculate the height (h) by using the equation:
h^2 + 20^2 = 26^2
This simplifies to:
h^2 + 400 = 676
Subtracting 400 from both sides:
h^2 = 676 - 400
h^2 = 276
Taking the square root of both sides:
h = √276
Therefore, the height of the platform is approximately:
h ≈ 16.6 feet
Since this is not an exact option in the multiple-choice answers provided, and assuming this is a rounding issue or real-world approximation, the closest answer is (a) 15 feet.