"Published in Newark, California, USA"
The Pennsylvania Railroad found it necessary, owing to land slides upon the roadbed, to reduce the angle of inclination of one bank of a certain railway cut near Pittsburgh, PA, from an original angle of 40° to a new angle of 25°. The bank as it originally stood was 200 ft. long and had a slant length of 60 ft. Find the amount of the earth removed, if the top level of the bank remained unchanged.
 |
| Photo by Math Principles in Everyday Life |
Solution:
Consider the given figure above
|
| Photo by Math Principles in Everyday Life |
From the two upper vertices of a triangle, draw vertical lines perpendicular to the ground and then label further the figure as follows
 |
| Photo by Math Principles in Everyday Life |
Consider a 40° right triangle,
The value of h in a 25° right triangle is equal to the value of h in a 40° right triangle.
Consider a 25° right triangle,
The length of the base of an obtuse triangle is
The area of an obtuse triangle which is the base of the prism is
Therefore, the amount of earth removed which is the volume of a prism is
