Expert: Sherry Wallin - 6/9/2011

Question
Workers at a mine have dug a tunnel that is 110 feet long and forms an angle of 38 degrees with the ground. A vertical shaft is dug. How long is the vertical shaft?

Answer
Hi Mary~

Let * represent the degree symbol, opp represent opposite, hyp represent hypotenuse

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~  <-- ground
       |  90*                                                38*    /
       |                                                                 /
       |                                                               /
       |                                                             /
   x  |                                                           / 110'
       |                                                         /
       |                                                       /
       |                                                     /     













these lines continue until they intersect below creating a right triangle
       
Let x = length of vertical shaft

sin 38* = x/110 =>     the sine of an angle equals the side opp divided by the hypotenuse; i.e., the opp side is x and the hyp is 110
x = 110(sin 38*) =>
x ~= 67.7'




       







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