Question

Find missing length and leave the a ser in radica form

Answer 1

The image is given below as

From the image above,

We have the given values as

`\begin{gathered} \theta=60^0 \\ hypotenus=2 \\ opposite=a \\ adjacent=b \end{gathered}`

Step 1:

To figure out the value of a, we will use the trigonometric ratio below

`\begin{gathered} \sin\theta=(opposite)/(hypotenu) \\ \sin60=(a)/(2) \\ cross\text{ multiply} \\ a=2\sin60 \\ a=2*(√(3))/(2) \\ a=√(3) \end{gathered}`

Hence,

The value of a is

`\Rightarrow a=√(3)`

Step 2:

To calculate the value of b, we will us ethe trigonometric ratio below

`\begin{gathered} \cos\theta=(adjacent)/(hypotenu) \\ \cos60^0=(b)/(2) \\ cross\text{ multiply, } \\ b=2\cos60 \\ b=2*(1)/(2) \\ b=1 \end{gathered}`

Hence,

The value of b is

`\Rightarrow b=1`