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.

Answer 1

The dimensions of the sides of the fruit stand are 3.5 feet , 2.0 feet  and 3.2 feet.

How to work with Law of Sines?

From the given image, we are given;

∠A = 35°; ∠B = 65°; c = 3.5 ft

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

∠A + ∠B + ∠C = 180

35 + 65 + ∠C = 180

∠C = 180 - (35 + 65)

∠C = 80°

From Law of sines;

a/sin A = b/sin B = c/sin C

Thus;

a = 3.5sin 35/sin 80

a = 2.04 ≈ 2

Thus;

b = 3.5sin 65/sin 80

b = 3.22 ≈ 3.2

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