# Triangle help - trigonometry

• Nov 17th 2009, 07:26 AM
refresh
Triangle help - trigonometry
A vertical pole 34 feet tall on a hillside that makes an angle of 13 degree with the horizontal. Determine the approximate length of a cable that would be needed to reach from the top of the pole to a point 57 feet downhill from the base of the pole.
• Nov 17th 2009, 07:44 AM
aidan
Quote:

Originally Posted by refresh
A vertical pole 34 feet tall on a hillside that makes an angle of 13 degree with the horizontal. Determine the approximate length of a cable that would be needed to reach from the top of the pole to a point 57 feet downhill from the base of the pole.

#1 Draw a sketch.
A rough sketch will often clear the fog.

The assumption is that the "57 feet downhill" is measured along the slope of the ground (and not horizontally from the base of the pole.)

The "point" will be
$\displaystyle 57 \sin(13deg) = 12.8$ feet BELOW the base of the pole; add that to the 34 feet to get the altitude of the triangle.
&
$\displaystyle 57 \cos(13deg) =$ 55.5 feet away from the center of the vertical pole; this is the base of the triangle.
then
the length of cable required = $\displaystyle \sqrt{ (34+12.8)^2 + (55.5)^2}$ is the hypotenuse of the triangle.

Does that help?
• Nov 17th 2009, 07:52 AM
refresh
72.65??