trigonometry i never took this and need help

Question

The problem: An important bed of coal dips at an angle of 20 degrees to the ground surface, which is horizontal. Where the bed crops out at the surface, the coal has been mined out. You are considering mining the coal underground. You have acquired the necessary permits and permission to dig a vertical mine shaft 2 km away from the surface outcrop.

How deep will you have to drill to reach the top of the coal bed? Assume that the surface is horizontal and strike and dip of the coal bed are constant. You’ll need to recall some basic trigonometric functions for this (for more information, go here). Be sure that you are calculating your data in degrees, not radians to arrive at the correct answer.

Answer 1

From the description of the problem, imagine the bed of coal as the hypotenuse of a right triangle with the surface as the base. The spot where you dig the vertical mine shaft is the vertex that makes a 90 degree angle. Since you know the angle the coal bed makes with the horizontal surface (20 degrees) and you know the distance between the outcrop and the site you want to build the mine shaft (2km), you can use tangent function to find the vertical distance you need to dig.

 

tan(20)= x/2

2tan(20)=x

x=0.7 km