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

Can you please help me with the answers, I don’t need the work I just need the answer-example-1
User Rwos
by
6.1k points

1 Answer

4 votes

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.

User Dangelsaurus
by
6.2k points
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