Question

determine the value of x and y your awsner must be in simplest radical form you cannot use sine cosine or tangent since those will give you decimal values

Answer 1

The Answer:

$x\text{ = 10, y = 20}$

Explanation:

Step 1: Since we cannot use Trigonometric tables, we have to use standard angles.

$\begin{gathered} \sin (60)\text{ = }\frac{10\sqrt[]{3}}{y} \\ \text{Therefore, make y the subject of the formula} \\ y\text{ = }\frac{\text{10}\sqrt[]{3\text{ }}}{\text{sin(60)}} \\ \sin (60)\text{ = }\frac{\sqrt[]{3}}{2}\text{ (according to standard angles)} \\ y\text{ = }\frac{\text{10}\sqrt[]{3}}{\frac{\sqrt[]{3}}{2}} \\ we\text{ can rewrite this as:} \\ y\text{ = 10}\sqrt[]{3}\text{ }\times\text{ }\frac{2}{\sqrt[]{3}} \\ \sqrt[]{3\text{ }}cancels\text{ out,} \\ y\text{ = 10}\times2\text{ = 20.} \end{gathered}$

Next we find the value of x this way:

$\begin{gathered} \cos \text{ 60 = }\frac{x}{y} \\ \text{But we already know that y = 20.} \\ \text{Therefore, we make x the subject of the formula;} \\ x=\text{ y}\times\cos \text{ 60 = 20 }\times\cos \text{ 60 } \\ x\text{ = 20 }\times\text{ }\frac{1}{2}\text{ = 10} \end{gathered}$

Thus, the values of x and y are 10 and 20 respectively.