This is an instance of solving a triangle using the law of cosines, which states that for any triangle with sides of length a, b, and c (where c is the side opposite the given angle), the following equation holds: c² = a² + b² - 2ab cos(C).
In this case:
a = 95 m
b = 110 m
C = 143°
We are asked to solve for c, or the rear property line.
c² = (95 m)² + (110 m)² - 2(95 m)(110 m) cos(143°)
cos(143°) is approximately -0.7431448254773942,
so
c² = 9025 m² + 12100 m² - 2(95 m)(110 m)(-0.7431448254773942)
c² = 9025 m² + 12100 m² +15538.70 m²
c² = 36663.70 m²
Taking the square root of both sides to solve for c gives approximately
c ≈ 191.47 m,
So, the length of the rear property line is approximately 191.47 meters.
He knows that his left and right boundary lines connect near his house at
an angle of 143°. The left boundary length is 95 m and the right is 110
m. Help the farmer determine the length of his rear property line.
1 answer