Final answer:
To find the height of the platform, we can use the Pythagorean theorem. The height of the platform is approximately 27.66 feet.
Step-by-step explanation:
To find the height of the platform, we can use the Pythagorean theorem. The ramp and the platform form a right triangle, with the length of the ramp as the hypotenuse and the height of the platform as one of the legs. The other leg represents the horizontal distance from the foot of the ramp to the bottom of the platform.
Using the Pythagorean theorem, we have: h^2 + 18^2 = 33^2, where h is the height of the platform. Simplifying the equation, we get: h^2 + 324 = 1089. Subtracting 324 from both sides, we have: h^2 = 1089 - 324, h^2 = 765. Taking the square root of both sides, we get: h = √765.
Therefore, the height of the platform is approximately 27.66 feet.