Choose the one alternative that best completes the statement or answers the question.
-A new homeowner has a triangular-shaped back yard. Two of the three sides measure $65 \mathrm { ft }$ and $80 \mathrm { ft }$ and form an included angle of $125 ^ { \circ }$. The owner wants to approximate the area of the yard, so that he can determine the amount of fertilizer and grass seed to be purchased. Find the area of the yard rounded to the nearest square foot.
A) $5200 \mathrm { sq }$. ft
B) $2130 \mathrm { sq } \cdot \mathrm { ft }$
C) $4260 \mathrm { sq } . \mathrm { ft }$
D) $2129 \mathrm { sq } . \mathrm { ft }$

Question

Quizplus · Accepted Answer

The area of a triangle with two sides $a$ and $b$ and an included angle $C$ is given by $\frac{1}{2}ab\sin(C)$. Substituting the given values: $\frac{1}{2} \times 65 \times 80 \times \sin(125^\circ) \approx 2130 \mathrm{sq} \cdot \mathrm{ft}$.

Choose the One Alternative That Best Completes the Statement or Answers