Final answer:
To calculate the length of the road in the tunnel with a 10° incline rising 1120 feet, use the sine function in the context of right-angled triangles. The formula L = 1120 ft/sin (10°) gives us the road length, which is approximately 6450 feet.
Step-by-step explanation:
We have to calculate the length of a road through a tunnel with a 10° incline rising to a height of 1120 feet. This problem can be solved by using the properties of right-angled triangles, where the height and the hypotenuse (the road) are two sides of the triangle, and the 10° angle gives us the ratio of these sides.
To solve for the length of the road (hypotenuse), we'll use the sine function which relates the opposite side (the height of 1120 ft) to the hypotenuse. The equation for the length (L) of the road is:
sin(10°) = height / L. Plugging in the values, we get sin(10°) = 1120 / L. We solve for L to find the length of the road that the trucks will travel.
Calculating, L = 1120 ft / sin(10°). Using a calculator, sin(10°) ≈ 0.1736. So, L ≈ 1120 / 0.1736 ≈ 6450.35 feet. Thus, the road through the tunnel will be approximately 6450 feet long.