Answer:
[tex]\sf \tan(A) & =\dfrac{9\sqrt{22}}{44}[/tex]
Step-by-step explanation:
If angle C is the right angle, then side c is the hypotenuse.
Use Pythagoras' Theorem [tex]a^2+b^2=c^2[/tex] to find the length of side a:
Given:
[tex]\implies a^2+(2 \sqrt{22})^2=13^2[/tex]
[tex]\implies a^2+88=169[/tex]
[tex]\implies a^2=81[/tex]
[tex]\implies a=\sqrt{81}[/tex]
[tex]\implies a=9[/tex]
Tan Trig Ratio
[tex]\sf \tan(\theta)=\dfrac{O}{A}[/tex]
where:
- [tex]\theta[/tex] is the angle
- O is the side opposite the angle
- A is the side adjacent the angle
Given:
- [tex]\theta[/tex] = A
- O = side opposite angle A = a = 9
- A = side adjacent angle A = b = 2√22
[tex]\begin{aligned}\implies \sf \tan(A) & =\dfrac{9}{2\sqrt{22}}\\\\ & =\dfrac{9}{2\sqrt{22}} \times \dfrac{\sqrt{22}}{\sqrt{22}}\\\\ & = \dfrac{9\sqrt{22}}{44} \end{aligned}[/tex]
