Question

In △MNP, m∠M=41∘, m∠P=62∘, and NP=108 centimeters.

What is MP?
Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.

cm

Answer 1

160.4 cm

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Answer 2

The length of MP is 160.4 cm

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,

`(\sin\angle M)/(NP)=(\sin\angle N)/(MP)=(\sin\angle P)/(MN)`

`(\sin41)/(108)=(\sin77)/(MP)=(\sin62)/(MN)`

`(\sin41)/(108)=(\sin77)/(MP)`

`MP=(\sin\angle 77)/(\sin \angle 41)* 108=160.400150515\sim 160.4 cm`

Hence, the length of MP is 160.4 cm