Final answer:
To find the angle of declination for the ramp, we can use the tangent function and the given lengths of the platform and wooden base. The angle of declination is approximately 77.75 degrees.
Step-by-step explanation:
To determine the angle of declination for the ramp to be built as a right triangle, we need to use trigonometric ratios. In this case, we are given the length of the platform (34 meters) and the length of the wooden base (21 feet). Since the platform is longer than the base, the ramp forms a right triangle. To find the angle of declination, we can use the tangent function. Tangent is defined as the ratio of the opposite side (platform) to the adjacent side (base): tan(angle) = opposite/adjacent.
Converting the length of the base to meters, we have 21 feet * 0.3048 meters/foot = 6.4016 meters. Plugging in the values, we get tan(angle) = 34 meters/6.4016 meters. Using a calculator, we find that the angle of declination is approximately 77.75 degrees.