Answer:
12.22 cm
Step-by-step explanation:
We'll be using cosine laws to solve for QR side:
[tex]\displaystyle{QR^2 = QP^2+RP^2-2QP\cdot RP \cdot \cos P}[/tex]
We know that QP = 13 cm, RP = 4 cm and cosP = 70°. Hence:
[tex]\displaystyle{QR^2=13^2+4^2-2(13)(4)\cos 70^{\circ}}[/tex]
Then evaluate the expression:
[tex]\displaystyle{QR^2=169+16-104 \cos 70^{\circ}}\\\\\displaystyle{QR^2=185-104\cos 70^{\circ}}\\\\\displaystyle{QR^2=185-35.57}[/tex]
Square root both sides, since length can only be positive. The negative side will be cancelled:
[tex]\displaystyle{\sqrt{QR^2}=\sqrt{185-35.57}}\\\\\displaystyle{QR=\sqrt{185-35.57}}\\\\\displaystyle{QR=12.22}[/tex]
Therefore, the length of QR will be around 12.22 cm or 12 cm when rounded to nearest integer.
