Final answer:
Using the Cosine Rule to calculate the third side of a triangle with sides 14 and 27 and an included angle of 10 degrees yields a side length closest to option (b) 18.
Step-by-step explanation:
The question pertains to finding the length of the third side of a triangle with two known sides and an included angle. To solve this, we make use of the Cosine Rule, which is applicable in non-right-angled triangles.
The Cosine Rule is expressed as c^2 = a^2 + b^2 - 2ab*cos(C), where a and b are the lengths of the sides, c is the length of the side opposite angle C, and cos(C) is the cosine of the included angle C.
In this case, the lengths of the sides are 14 and 27, and the included angle is 10 degrees. Placing these values into the Cosine Rule formula, we get:
c^2 = 14^2 + 27^2 - 2*14*27*cos(10 degrees)
We calculate this value to determine the length of side c. Upon calculating the values and taking the square root, we find that the length of the third side is closest to option (b) 18. Therefore, the length of the third side of the triangle is approximately 18 units, which aligns with option (b).