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: [tex]\angle A=35^{\circ}[/tex], [tex]\angle B=65^{\circ}[/tex] and [tex]c=3.5ft[/tex].
According to the angle sum property of a triangle, the sum of all interior angles of a triangle is 180 degree.
[tex]\angle A+\angle B+\angle C=180^{\circ}[/tex]
[tex]35^{\circ}+65^{\circ}+\angle C=180^{\circ}[/tex]
[tex]\angle C=180^{\circ}-100^{\circ}[/tex]
[tex]\angle C=80^{\circ}[/tex]
According to Law of sines
[tex]\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]
[tex]\frac{a}{\sin A}=\frac{c}{\sin C}[/tex]
[tex]\frac{a}{\sin 35}=\frac{3.5}{\sin 80}[/tex]
[tex]a=\frac{3.5}{\sin 80}\times \sin 35[/tex]
[tex]a=2.04[/tex]
[tex]a\approx 2.0[/tex]
[tex]\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]
[tex]\frac{b}{\sin 65}=\frac{3.5}{\sin 80}[/tex]
[tex]b=\frac{3.5}{\sin 80}\times \sin 65[/tex]
[tex]b=3.22[/tex]
[tex]b\approx 3.2[/tex]
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.
