Question

Find the exact value of sin G.A. √1010B. 3√1010C. 4√10D. 160

Answer 1

Given the Right Triangle EFG, you know that:

`\begin{gathered} EF=4 \\ EG=12 \end{gathered}`

By definition:

`sin\theta=(opposite)/(hypotenuse)`

Since, in this case:

`\theta=G`

You can identify that:

`\begin{gathered} opposite=EF=4 \\ hypotenuse=FG \end{gathered}`

In order to find the hypotenuse of the Right Triangle, you need to use the Pythagorean Theorem, which states that:

`c=√(a^2+b^2)`

Where "c" is the hypotenuse, and "a" and "b" are the legs of the Right Triangle.

You can set up that:

`\begin{gathered} c=FG \\ a=EG=12 \\ b=EF=4 \end{gathered}`

Therefore:

`FG=√(12^2+4^2)=4√(10)`

Now you can determine that:

`sinG=(4)/(4√(10))`

Simplify:

`sinG=(1)/(√(10))`

You can multiply the numerator and the denominator by:

`√(10)`

In order to Rationalize the denominator:

`sinG=(1\cdot√(10))/(√(10)\cdot√(10))`
`sinG=(1\cdot√(10))/((√(10))^2)`
`sinG=(√(10))/(10)`

Hence, the answer is: Option A.