Question

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

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

Answer 1

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

Step-by-step 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.