Question

The owner of a Farmer’s Market wants to construct a triangular fruit stand in his store. Use the diagram below and the Law of Sines to determine the dimensions of the sides of the fruit stand.
A. 3.5 x 6 x 3.8
B. 3.5 x 2 x 3..2
C. 3.5 x 2.9 x 3.3
D. 3.5 x 2.5 x 3.4

Please select the best answer from the choices provided

Answer 1

Hello,
Please, see the attached file.
Thanks.

Answer 2

Answer:

The dimensions of the sides of the fruit stand are 3.5 feet , 2.0 feet  and 3.2 feet. Option B is correct.

Step-by-step explanation:

Given information: $\angle A=35^{\circ}$, $\angle B=65^{\circ}$ and $c=3.5ft$.

According to the angle sum property of a triangle, the sum of all interior angles of a triangle is 180 degree.

$\angle A+\angle B+\angle C=180^{\circ}$

$35^{\circ}+65^{\circ}+\angle C=180^{\circ}$

$\angle C=180^{\circ}-100^{\circ}$

$\angle C=80^{\circ}$

According to Law of sines

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

$\frac{a}{\sin A}=\frac{c}{\sin C}$

$\frac{a}{\sin 35}=\frac{3.5}{\sin 80}$

$a=\frac{3.5}{\sin 80}\times \sin 35$

$a=2.04$

$a\approx 2.0$

$\frac{b}{\sin B}=\frac{c}{\sin C}$

$\frac{b}{\sin 65}=\frac{3.5}{\sin 80}$

$b=\frac{3.5}{\sin 80}\times \sin 65$

$b=3.22$

$b\approx 3.2$

Therefore the dimensions of the sides of the fruit stand are 3.5 feet , 2.0 feet  and 3.2 feet. Option B is correct.