High School

A triangular plot of land is enclosed by a fence. One side is 30.3 m long, and an adjacent side is 18.5 m long. The included angle between the two sides is 61 degrees. Determine the length of the third side of the fence to the nearest tenth of a meter.

A) 23.2 m
B) 29.7 m
C) 49.4 m
D) 51.7 m

Answer :

Final answer:

The third side of the fence is approximately 23.2 meters long. So, the correct answer is A.

Explanation:

To find the third side of the fence, we can use the law of cosines. The law of cosines states that for a triangle with sides a, b, and c, and the angle between sides a and b denoted by α, the third side c can be found using the formula:

c = sqrt(a^2 + b^2 - 2ab * cos(α))

Using the given information, we can substitute the known values into the formula:

c = sqrt(30.3^2 + 18.5^2 - 2 * 30.3 * 18.5 * cos(61))

c ≈ 23.2m

So, the correct answer is A.

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