Answer:
[tex]x = \frac{16\sqrt{3}}{3}[/tex]
[tex]y = \frac{32\sqrt 3}{3}[/tex]
Step-by-step explanation:
Calculating (x):
Here, we make use of the tan formula
[tex]tan\theta = \frac{Opp}{Adj}[/tex]
Where
[tex]\theta = 60[/tex]
[tex]Opp = 16[/tex]
[tex]Adj = x[/tex]
This gives:
[tex]tan\ 60= \frac{16}{x}[/tex]
Make x the subject
[tex]x = \frac{16}{tan\ 60}[/tex]
tan(60) in surd form is [tex]\sqrt{3}[/tex]
So:
[tex]x = \frac{16}{\sqrt{3}}[/tex]
Rationalize
[tex]x = \frac{16}{\sqrt{3}} * \frac{\sqrt{3}}{\sqrt{3}}[/tex]
[tex]x = \frac{16\sqrt{3}}{3}[/tex]
Calculating (y):
Here, we make use of the tan formula
[tex]sin\theta = \frac{Opp}{Hyp}[/tex]
Where
[tex]\theta = 60[/tex]
[tex]Opp = 16[/tex]
[tex]Hyp= y[/tex]
This gives:
[tex]sin\ 60= \frac{16}{y}[/tex]
Make y the subject
[tex]y= \frac{16}{sin\ 60}[/tex]
tan(60) in surd form is [tex]\frac{\sqrt{3}}{2}[/tex]
[tex]y= \frac{16}{\frac{\sqrt{3}}{2}}[/tex]
[tex]y = 16/\frac{\sqrt 3}{2}[/tex]
[tex]y = 16*\frac{2}{\sqrt 3}[/tex]
[tex]y = \frac{32}{\sqrt 3}[/tex]
Rationalize
[tex]y = \frac{32}{\sqrt 3}*\frac{\sqrt 3}{\sqrt 3}[/tex]
[tex]y = \frac{32\sqrt 3}{3}[/tex]
