SOLUTION: A triangular beach lot has a frontage on the sea of 100 yards. The boundary lines running from the beach make on the inner side of lot angles of 60degrees and 50degrees respectivel

Algebra ->  Triangles -> SOLUTION: A triangular beach lot has a frontage on the sea of 100 yards. The boundary lines running from the beach make on the inner side of lot angles of 60degrees and 50degrees respectivel      Log On


   

Question 890855: A triangular beach lot has a frontage on the sea of 100 yards. The boundary lines running from the beach make on the inner side of lot angles of 60degrees and 50degrees respectively with the shore line. Determine the distance of the dividing line from the vertex of the triangle to the opposite side along the shore line to divide the lots into two equal areas.
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Imagine or draw this:
Triangle with base side 100, on the left a side making angle 60 degrees with the base, on the right
a side making angle 50 degrees with the base.

The vertex opposite of the base side is angle of measure 180-60-50=highlight_green%2870%29 degrees.

Law of Sines can give either or both of the non-given sides. Picking the side on the left,
sine%2850%29%2FL=sine%2870%29%2F100 where L is the length of the ungiven side at the left of the triangle.

L%2Fsin%2850%29=100%2Fsine%2870%29

highlight_green%28L=100%28sin%2850%29%2Fsin%2870%29%29%29

The question's meaning is to find the length from the 70 degree vertex to the base side,
which the altitude from that vertex. This cuts the triangle into two right triangles.

Altitude is L%2Asin%2860%29, basic trigonometry.
Altitude is highlight%28100%2Asin%2860%29%28sin%2850%29%2Fsin%2870%29%29%29.