Question

a zoo is building a new giraffe exhibit and needs to fence an outdoor triangular​ area, with the barn forming one side of the triangle. The maintenance department only has 127 ft of fencing in stock. If one of the sides of the outdoor pen is 73 ft and the angle that makes with the barn is 72 degrees, does the zoo need to order more fencing

Answer 1

Yes, the zoo needs to order more fencing. The zoo has 54 ft of fence remaining for the unknown side.

If the unknown side is assumed to have this length, sin (θ) = 1.2857. which is not possible, so the triangle cannot be formed.

Explanation:

Let a be the length of the third side of the triangle.

a = 127 - 73 = 54 ft

Let the angle that a makes with the barn be θ

The diagram of this question is attached to this solution.

Using the sine rule, we can examine if the remaining fencing material would be enough by checking if (sin θ) is realistic.

Using sine rule,

[a/(sin 72°)] = [73/(sin θ)]

[54/sin 72°] = [73/sin θ]

sin θ = (73 × sin 72°)/54 = 1.2857

sin θ = 1.2857

This is obviously not a realistic value for sin θ since it is known that sin θ ranges between 0 and 1.

The 54 ft is obviously not enough.

Hence, the zoo needs more fencing material to be able to complete the outdoor triangular giraffe exhibit.

Hope this Helps!!!