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

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

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

`(a)/(\sin A)=(b)/(\sin B)=(c)/(\sin C)`

`(a)/(\sin A)=(c)/(\sin C)`

`(a)/(\sin 35)=(3.5)/(\sin 80)`

`a=(3.5)/(\sin 80)* \sin 35`

`a=2.04`

`a\approx 2.0`

`(b)/(\sin B)=(c)/(\sin C)`

`(b)/(\sin 65)=(3.5)/(\sin 80)`

`b=(3.5)/(\sin 80)* \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.

Answer 2

Hello,
Please, see the attached file.
Thanks.