Question

If ∠R measures 18°, q equals 9.5, and p equals 6.0, then which length can be found using the Law of Cosines?

Option 1: RQ
Option 2: PQ
Option 3: p
Option 4: q

Answer 1

Using the Law of Cosines with the given angle ∠R and sides p and q, the length of side PQ can be determined. The formula c² = a² + b² - 2ab * cos(C) will give the squared value of PQ, which upon taking the square root will return the actual length.

Step-by-step explanation:

If ∠R measures 18°, q equals 9.5, and p equals 6.0, the length that can be found using the Law of Cosines is Option 2: PQ. The Law of Cosines is used to find the length of a side in a triangle when you know the lengths of the other two sides and the measure of the included angle. In this case, sides p and q and the angle between them, ∠R, are known.

The formula for the Law of Cosines is c² = a² + b² - 2ab * cos(C), where c is the side opposite the angle C, and a and b are the other two sides of the triangle. Here, p and q would be a and b, and PQ would be c. The calculation would be as follows:

• PQ² = p² + q² - 2pq * cos(∠R)
• PQ² = 6.0² + 9.5² - 2(6.0)(9.5) * cos(18°)
• PQ = sqrt(PQ²)

The lengths RQ, p, and q are already given or defined and cannot be 'found' in this context, which makes Option 2 the correct answer.