The length side of a triangle PQR is 14.5 cm <PQR=71,<PQR=57,find the length of the sides PR and PQ
You cannot have both <PQR=71 and <PQR=57
Also, since we do not know which side of the triangle is 14.5, we cannot solve for the other parts.
Apologies for the confusion. You're right, it's not possible to have both <PQR=71 and <PQR=57. Additionally, without knowing which side of the triangle is 14.5 cm, we cannot determine the lengths of the other sides of the triangle. Therefore, we do not have enough information to solve for the lengths of sides PR and PQ.
To find the lengths of sides PR and PQ, we can use the Law of Cosines.
The Law of Cosines states that for any triangle with sides a, b, and c and angle C opposite side c, we have:
c^2 = a^2 + b^2 - 2ab*cos(C)
In this case, we know that side QR has a length of 14.5 cm, and angle PQR is 71 degrees, and angle QPR is 57 degrees.
Let's find the length of side PR first:
PR^2 = PQ^2 + QR^2 - 2PQ*QR*cos(PQR)
PR^2 = PQ^2 + (14.5)^2 - 2*PQ*14.5*cos(71)
Similarly, we can find the length of side PQ:
PQ^2 = PR^2 + QR^2 - 2PR*QR*cos(QPR)
Now we have two equations with two unknowns, PR and PQ. We can solve these equations simultaneously to find the lengths of the sides.
However, without the actual values for PQ^2 + QR^2 - 2PQ*QR*cos(71) and PR^2 + QR^2 - 2PR*QR*cos(57), we cannot find the precise lengths of sides PR and PQ.