Answer:
The value of tan(G) in the right triangle GYK Is [tex]\sqrt{3}[/tex]
Step-by-step explanation:
Given
Measure of angle at [tex]G=60^{\circ}[/tex]
Measure of angle at [tex]Y=30^{\circ}[/tex]
Measure of angle at [tex]K=90^{\circ}[/tex]
To find:
[tex]\tan (G)=?[/tex]
Solution:
In trigonometry we know that
[tex]\tan G=\frac{\sin G}{\cos G}[/tex]
[tex]G=60^{\circ}[/tex]
So,
[tex]\sin (60)=\frac{\sqrt{3}}{2}[/tex]
[tex]\cos (60)=\frac{1}{2}[/tex]
Substituting in the formula we have,
[tex]\tan G=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}[/tex]
[tex]\tan G=\frac{\sqrt{3}}{2} \times \frac{2}{1}[/tex]
[tex]\tan G=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}[/tex]
[tex]\tan G=\sqrt{3}[/tex]
Result:
Thus the value of [tex]\tan G=\sqrt{3}[/tex]
