Question

two sides of a parallelogram are 32 feet and 77 feet. the measure of the angle between these sides is 16°. find the area of the parallelogram to the nearest square foot.

Explanation:

Step1: Recall area formula for parallelogram

The area $A$ of a parallelogram with sides $a$, $b$ and included angle $\theta$ is $A = a \cdot b \cdot \sin(\theta)$.

Step2: Substitute given values

Here, $a=32$, $b=77$, $\theta=16^\circ$.
$A = 32 \times 77 \times \sin(16^\circ)$

Step3: Calculate $\sin(16^\circ)$ and compute

$\sin(16^\circ) \approx 0.2756$
$A \approx 32 \times 77 \times 0.2756$
$A \approx 2464 \times 0.2756 \approx 679.0784$

Step4: Round to nearest square foot

Round $679.0784$ to the nearest whole number.

Answer:

679 square feet