Answer:
D.
[tex]u =3[/tex]
[tex]v =\sqrt{3}[/tex]
Step-by-step explanation:
Given
The triangle in the diagram above
Required
Find the missing lengths, u and v
To find the missing lengths, we have to check the relationship between the missing lengths, the given length and the given angle;
From trigonometry;
[tex]sin\ \theta = \frac{Opp}{Hyp}[/tex]; Where Opp = Opposite and Hyp = Hypotenuse
From the attached diagram;
[tex]\theta = 30[/tex]
[tex]Opp = v[/tex]
[tex]Hyp = 2\sqrt{3}[/tex]
[tex]sin\ \theta = \frac{Opp}{Hyp}[/tex] becomes
[tex]sin\ 30 = \frac{v}{2\sqrt{3}}[/tex]
Multiply both sides by [tex]2\sqrt{3}[/tex]
[tex]2\sqrt{3} * sin\ 30 = \frac{v}{2\sqrt{3}} * 2\sqrt{3}[/tex]
[tex]2\sqrt{3} * sin\ 30 = v[/tex]
In radians, [tex]sin30 = \frac{1}{2}[/tex]
[tex]2\sqrt{3} * \frac{1}{2} = v[/tex]
[tex]\sqrt{3} = v[/tex]
[tex]v =\sqrt{3}[/tex]
Similarly, From trigonometry;
[tex]cos\ \theta = \frac{Adj}{Hyp}[/tex]; Where Adj = Adjacent
From the attached diagram;
[tex]\theta = 30[/tex]
[tex]Adj = u[/tex]
[tex]Hyp = 2\sqrt{3}[/tex]
[tex]cos\ \theta = \frac{Adj}{Hyp}[/tex] becomes
[tex]cos\ 30 = \frac{u}{2\sqrt{3}}[/tex]
Multiply both sides by [tex]2\sqrt{3}[/tex]
[tex]2\sqrt{3} * cos\ 30 = \frac{u}{2\sqrt{3}} * 2\sqrt{3}[/tex]
[tex]2\sqrt{3} * cos\ 30 = u[/tex]
In radians, [tex]cos30 = \frac{\sqrt{3}}{2}[/tex]
[tex]2\sqrt{3} * \frac{\sqrt{3}}{2} = u[/tex]
[tex]\sqrt{3} * \sqrt{3} = u[/tex]
[tex]3 = u[/tex]
[tex]u =3[/tex]
