Question

PLEASE HELP! Given: △MNO m∠M=45°, m∠O=30° MN=6 Find: NO, MO.

Answer 1

Answer:

NO = 8.48 units, MO = 11.59 Units

Step-by-step explanation:

∠M = 45°

∠O = 30°

∠N = 180-(45+30)

∠N = 105°

MN=6 = o

NO = m

MO = n

From sine rule

$\frac{sinM}{m}=\frac{sinN}{n}=\frac{sinO}{o}$

$\\\Rightarrow \frac{sinO}{o}=\frac{sinM}{m}\\\Rightarrow m=\frac{sinM}{\frac{sinO}{o}}\\\Rightarrow m=\frac{sin45}{\frac{sin30}{6}}\\\Rightarrow m=8.48$

$\frac{sinO}{o}=\frac{sinN}{n}\\\Rightarrow n=\frac{sinN}{\frac{sinO}{o}}\\\Rightarrow n=\frac{sin105}{\frac{sin30}{6}}\\\Rightarrow n=11.59$

∴ NO = 8.48 units, MO = 11.59 Units