A pier forms an 85° angle with a straight shore. At a distance of 100 feet from the pier, the line of sight to the tip forms a 37° angle. Find the length of the pier to the nearest tenth of a foot.

Question

amistre64 · Answer

100 feet which way?  of the pier is at a slant of 85 degrees, then are we 100 feet into the acute or the obtuse angle?

amistre64 · Answer

ill assume the acute angle; and use the law of sines.

we are given 2 angles for the triangle and the length of one side (100ft).  We find the missing angle by:

180 - a - b = c

180 - 37 - 85 = 58 degrees.

the law of sines says the sinA/a = sinB/b = sinC/c

angles are in degrees...

sin(37)      sin(58)
-----  =  -------
  x              100

x = 100 sin(37)/sin(58)

the pier is:  70.96  barring any unforseen errors in computations :)