Answer:
The length of MP is 160.4 cm
Step-by-step explanation:
Given △MNP, m∠M=41∘, m∠P=62° and NP=108 cm
we have to find the length of MP.
In ΔMNP, by amgle sum property
m∠M+m∠N+m∠P=180°
41°+m∠N+62°=180°
m∠N=180°-41°-62°=77°
By sine law,
[tex]\frac{\sin\angle M}{NP}=\frac{\sin\angle N}{MP}=\frac{\sin\angle P}{MN}[/tex]
[tex]\frac{\sin41}{108}=\frac{\sin77}{MP}=\frac{\sin62}{MN}[/tex]
[tex]\frac{\sin41}{108}=\frac{\sin77}{MP}[/tex]
[tex]MP=\frac{\sin\angle 77}{\sin \angle 41}\times 108=160.400150515\sim 160.4 cm[/tex]
Hence, the length of MP is 160.4 cm
