Question

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

Answer 1

Answer:

12.22 cm

Step-by-step 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:

$\displaystyle{\sqrt{QR^2}=\sqrt{185-35.57}}\\\\\displaystyle{QR=\sqrt{185-35.57}}\\\\\displaystyle{QR=12.22}$

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