Final answer:
Using trigonometry with the 30 degrees angle of elevation and the 8 feet height of the platform, the length of the ramp can be determined to be 16 feet.
Step-by-step explanation:
To determine the length of the ramp that a construction worker is building, we can use trigonometry. The worker must construct a ramp with an angle of elevation of 30 degrees to span the vertical distance of 8 feet between the upper and lower platforms. The length of the ramp is the hypotenuse of a right-angled triangle where the opposite side is the height of the platform and the angle given is the angle of elevation.
The mathematical relationship we will use is derived from the sine function, which is defined as the ratio of the opposite side to the hypotenuse in a right-angled triangle. Therefore, we have:
Sin(θ) = opposite / hypotenuse
Plugging in the values we have:
Sin(30°) = 8 ft / hypotenuse
Since the sine of 30 degrees is 0.5, the equation becomes:
0.5 = 8 ft / hypotenuse
To find the length of the hypotenuse (ramp), we solve for the hypotenuse:
hypotenuse = 8 ft / 0.5
hypotenuse = 16 ft
Therefore, the length of the ramp is 16 feet.