Question

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 2222degrees° angle with the road. How long are the other two​ sides?

Answer 1

Answer:

81.23 ft and 77.88 ft long

Step-by-step 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:

$\frac{A}{sin(a)}= \frac{B}{sin(b)}= \frac{C}{sin(c)}$

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

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

The other two sides are 81.23 ft and 77.88 ft long