Question

PLS HELP PLS
Determine the length of side QR in the following triangle

Answer 1

12.22 cm

Explanation:

We'll be using cosine laws to solve for QR side:

`\displaystyle{QR^2 = QP^2+RP^2-2QP\cdot RP \cdot \cos P}`

We know that QP = 13 cm, RP = 4 cm and cosP = 70°. Hence:

`\displaystyle{QR^2=13^2+4^2-2(13)(4)\cos 70^(\circ)}`

Then evaluate the expression:

`\displaystyle{QR^2=169+16-104 \cos 70^(\circ)}\\\\\displaystyle{QR^2=185-104\cos 70^(\circ)}\\\\\displaystyle{QR^2=185-35.57}`

Square root both sides, since length can only be positive. The negative side will be cancelled:

`\displaystyle{√(QR^2)=√(185-35.57)}\\\\\displaystyle{QR=√(185-35.57)}\\\\\displaystyle{QR=12.22}`

Therefore, the length of QR will be around 12.22 cm or 12 cm when rounded to nearest integer.