A triangular plot of land has one side along a straight road measuring 147147 feet. A second side makes a 2323degrees° angle with the road, and the third side makes a 2222degre…

Question

asked Jun 21, 2021 74.2k views

1 Answer

Martin Mlostek · Answer 1 · 2021-06-28T06:03:12+0000

Answer:

81.23 ft and 77.88 ft long

Explanation:

The sum of the internal angles of a triangle is 180 degrees, the missing angle is:

$a+b+c=180\\a+23+22=180\\a=135^o$

According to the Law of Sines:

(A)/(sin(a))= (B)/(sin(b))= (C)/(sin(c))

Let A be the side that is 147 feet long, the length of the other two sides are:

$(A)/(sin(a))= (B)/(sin(b))\\B=(sin(23)*147)/(sin(135))\\B=81.23\ ft\\\\(A)/(sin(a))= (C)/(sin(c))\\C=(sin(22)*147)/(sin(135))\\C=77.88\ ft$

The other two sides are 81.23 ft and 77.88 ft long