Question

In ΔPQR, mP = 33, mQ = 82, and PR = 14.2. To the nearest tenth, what is the length of QR ?

Answer 1

Answer:

7.8 units

Step-by-step explanation:

Given: In ΔPQR, m∠P = 33, m∠Q = 82, and PR = 14.2.

Law of sine:

$\dfrac{a}{\sin A}=\dfrac{b}{\sin b}=\dfrac{c}{\sin C}$

Using law of sine, we get

$\dfrac{QR}{\sin P}=\dfrac{PR}{\sin Q}$

$\dfrac{QR}{\sin (33)}=\dfrac{14.2}{\sin (82)}$

$\frac{QR}{0.544639}=\frac{14.2}{0.990268}$

$QR=\frac{14.2}{0.990268}\times 0.544639$

$QR=7.809879$

$QR\approx 7.8$

Therefore, the length of QR is 7.8 units.