Design+A+Road

Workers are designing a road to go over a mountain. They wan the road to have a maximum grade of 14%. The lowest gap in the mountain that they are going to go over has an elevation of 1625 feet above sea level. The road will start at an elevation of 414 feet above sea level and meet up with a road on the other side at the elevation of 633 feet above sea level. What is the minimum length of the road to meet these requirements? What is the average angle of elevation for this road?

~ To solve this problem we set up 2 similar triangles and figured out the lengths of all the sides and the angle mesures.(See diagram bellow) ~ When we made the 2 similar triangles we solved them because of equal angles. (See diagram bellow) ~ The bellow diagram shows how we took the Maximum Grade percentage and turned it into the angle we used for the similar triangles ~ In the diagram we used the Inverse Trig Functions to find the missing angles when we found the sides. We found the sides by subtracting the highest point of the mountain the the lowest point on each side. The diagram bellow shows all the steps in which we took to find all of the sides and all of the angle mesurments.

To answer the questions up top, the minimum length of the road that meets the requirements is 15,891 feet long. The average angle of elevation would be 7.97 degrees.



This picture shows a road in a mountain, what we did was, hypothetically speaking, pulled it completly straight through the mountain and found the shortest way to create the road.

//**__Justinz WORK!__**//

Workers are designing a road to go over a mountain. They want the road to have a maximum grade of 14%. The lowest gap in the mountain that they are going to go over has an elevation of 1625 feet above sea level. The road will start at an elevation of 414 feet above sea level and meet up with a road on the other side at the elevation of 633 feet above sea level. What is the minimum length of the road to meet these requirements? What is the average angle of elevation for this road?

To solve this problem we set up 2 similar triangles and figured out the lengths of all the sides and the angle measures.

Angle Solving Aqui! To solve for the angles we took the Opp. divided by Hyp. to get the sine of angle c(smallest angle), then multiplied by the reciprocal of sine, then subtracted those two angle measures to get the last angles.