Question

Find all the missing elements:
B
14
15
70°
A
b
с

Answer 1

`B=48.7\\`

`c=61.3`

`b=12`

Explanation:

Using sines law for triangles,

`(15)/(sinA) =(14)/(sinc) =(b)/(sinB) \\\\A= 70`

⇒
`(15)/(sin70) =(14)/(sinC) =(b)/(sinB)`

⇒
`(15)/(0.9397) =(14)/(sinC)=(b)/(sinB)`

⇒
`15.9625=(14)/(sinC)`

⇒
`SinC=(14)/(15.9625)=0.8771`

⇒
`C=Sin^(-1)(0.8771)=61.29`

⇒
`C=61 ~ or ~ 61.30`

`(b)/(Sin B)=15.9625`

Now sum of angles a Δ is 180°

A+B+C=180°

`70+B+61=180`

`B=180-131=49~ or ~ 48.7`

`b=sin(48.70)(15.9625)=(0.7547)*(15.9625)= 12.0`

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hope it helps..

have a great day!!

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