Question

In ΔMNO, n = 49 inches, m = 94 inches and ∠M=62°. Find all possible values of ∠N, to the nearest 10th of a degree.

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Answer 1

Therefore the value of ∠
`N` is
`27`°.

Therefore the value of ∠
`O` is
`91`°.

Explanation:

Given that,

`MNO` is a triangle.

`n=49\ inches`,
`m=94\ inches`, and ∠
`M=62`°

and we have to find the value of ∠
`N`.

Diagram of the Δ
`MNO` is shown below:

Now,

According to Law of Sine,
`(m)/(sinM) =(n)/(sinN) =(o)/(sinO)`

⇒
`(m)/(sinM)=(n)/(sinN)`

⇒
`(94)/(sin62) =(49)/(sinN)`

⇒
`(94)/(0.88295) =(49)/(sinN)`

⇒
`sinN*94=49*0.88295`

⇒
`sinN=(43.26455)/(94) =0.46026`

⇒
`N=sin^(-1)(0.46026)`

∴∠
`N=27`°

Therefore the value of ∠
`N` is
`27`°.

In Δ
`MNO`,

∠
`M+`∠
`N+`∠
`O=180`° [Angle sum property]

⇒
`62`°
`+27`°
`+`∠
`O=180`°

⇒ ∠
`O=91`°

Therefore the value of ∠
`O` is
`91`°.