Question

InAABC,a = 13, and bFind c to the nearesttenth.AmZA = 19°,b= 14.Baс

Answer 1

Given:

`m\angle A=19\degree,a=13\text{ and b=14.}`

Required:

We need to find the value of c.

Step-by-step explanation:

Consider the sine law.

`(sinA)/(a)=(sinB)/(b)`
`Substitute\text{ }m\angle A=19\degree,a=13\text{ and b=14 in the formula,}`
`(sin19\degree)/(13)=(sinB)/(14)`
`(sin19\degree)/(13)*14=(sinB)/(14)*14`
`(sin19\degree)/(13)*14=sinB`
`sinB=(sin19\degree)/(13)*14`
`sin^(-1)sinB=sin^(-1)((sin19\degree)/(13)*14)`
`B=sin^(-1)((sin19\degree)/(13)*14)`
`m\angle B=20.5\degree`

Use the triangle sum properly.

`m\angle A+m\angle B+m\angle C=180\degree`
`Substitute\text{ }m\angle A=19\degree,and\text{ }m\angle B=20.5\text{ in the formula.}`
`19\degree+20.5\degree+m\angle C=180\degree`
`39.5\degree+m\angle C=180\degree`
`39.5\degree+m\angle C-39.5\degree=180\degree-39.5\degree`
`m\angle C=140.5\degree`

Consider the sine law.

`(sinA)/(a)=(sinC)/(c)`
`Substitute\text{ }m\angle A=19\degree,a=13\text{ and }m\angle C=140.5\text{ in the formula,}`
`(sin19\degree)/(13)=(sin140.5\degree)/(c)`
`(13)/(sin19\degree)=(c)/(sin140.5\degree)`
`(13)/(sin19\degree)* sin140.5\degree=(c)/(sin140.5\degree)* sin140.5\degree`
`(13)/(sin19\degree)* sin140.5\degree=c`
`c=25.3987`
`c=25.4`

Final answer:

`c=25.4units`