Answer:
[tex]x=4[/tex]
Step-by-step explanation:
We have been given an image of two right triangles and we asked to find the value of x.
First of all , we will find the length of segment RT using sine.
[tex]\text{Sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}[/tex]
Upon substituting our given values in above formula we will get,
[tex]\text{Sin}(60^{\circ})=\frac{2\sqrt{3}}{RT}[/tex]
[tex]RT=\frac{2\sqrt{3}}{\text{Sin}(60^{\circ})}[/tex]
[tex]RT=\frac{2\sqrt{3}}{\frac{\sqrt{3}}{2}}[/tex]
[tex]RT=\frac{2\sqrt{3}}{\sqrt{3}}\times 2[/tex]
[tex]RT=2\times 2[/tex]
[tex]RT=4[/tex]
Now we know that length of segment RT and angle QRT of triangle QRT, so we will use tangent to find the length of segment QR (x) as:
[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]
[tex]\text{tan}(45^{\circ})=\frac{x}{4}[/tex]
Multiplying both sides of our equation by 4 we will get,
[tex]\text{tan}(45^{\circ})*4=\frac{x}{4}*4[/tex]
[tex]\text{tan}(45^{\circ})*4=x[/tex]
Substituting [tex]\text{tan}(45^{\circ})=1[/tex] we will get,
[tex]1*4=x[/tex]
[tex]4=x[/tex]
Therefore, the value of x is 4 units.
