Question

Can you please help me with the answers, I don’t need the work I just need the answer please

Answer 1

Given that

The angles of the triangle are

30, 60 and 90

Consider the sine law formula

`(a)/(\sin A)=(b)/(\sin B)=(c)/(\sin C)`

Let A=30, B=60, and C=90, and substitute these values in the sine law, we get

`(a)/(\sin 30^o)=(b)/(\sin 60^o)=(c)/(\sin 90^o)`

`(a)/((1)/(2))^{}=\frac{b}{\frac{\sqrt[]{3}}{2}}=(c)/(1)`

The ratio of the legs a and b is

`(a)/(b)=\frac{(1)/(2)}{\frac{\sqrt[]{3}}{2}}=(1)/(2)*\frac{2}{\sqrt[]{3}}=\frac{1}{\sqrt[]{3}}`
`1\colon\sqrt[]{3}`

The ratio of the legs b and c is

`(b)/(c)=\frac{\frac{\sqrt[]{3}}{2}}{1}=\frac{\sqrt[]{3}}{2}`
`\sqrt[]{3}\colon2`

The ratio of the legs a and c is

`(a)/(c)=((1)/(2))/(1)=(1)/(2)`
`1\colon2`

Hence the answer is

`1\colon\sqrt[]{3}`

Option C is correct.