Answer :
Answer:
Therefore the value of ∠[tex]N[/tex] is [tex]27[/tex]°.
Therefore the value of ∠[tex]O[/tex] is [tex]91[/tex]°.
Step-by-step explanation:
Given that,
[tex]MNO[/tex] is a triangle.
[tex]n=49\ inches[/tex], [tex]m=94\ inches[/tex], and ∠[tex]M=62[/tex]°
and we have to find the value of ∠[tex]N[/tex].
Diagram of the Δ[tex]MNO[/tex] is shown below:
Now,
According to Law of Sine, [tex]\frac{m}{sinM} =\frac{n}{sinN} =\frac{o}{sinO}[/tex]
⇒ [tex]\frac{m}{sinM}=\frac{n}{sinN}[/tex]
⇒ [tex]\frac{94}{sin62} =\frac{49}{sinN}[/tex]
⇒ [tex]\frac{94}{0.88295} =\frac{49}{sinN}[/tex]
⇒ [tex]sinN\times94=49\times0.88295[/tex]
⇒ [tex]sinN=\frac{43.26455}{94} =0.46026[/tex]
⇒ [tex]N=sin^{-1}(0.46026)[/tex]
∴∠[tex]N=27[/tex]°
Therefore the value of ∠[tex]N[/tex] is [tex]27[/tex]°.
In Δ[tex]MNO[/tex],
∠[tex]M+[/tex]∠[tex]N+[/tex]∠[tex]O=180[/tex]° [Angle sum property]
⇒ [tex]62[/tex]°[tex]+27[/tex]°[tex]+[/tex]∠[tex]O=180[/tex]°
⇒ ∠[tex]O=91[/tex]°
Therefore the value of ∠[tex]O[/tex] is [tex]91[/tex]°.
