Respuesta :
Using it's formula, it is found that the tangent of F is given by:
- [tex]\tan{F} = \frac{6\sqrt{85}}{85}[/tex]
How to find the tangent of an angle?
- In a right triangle, the tangent of an angle is given by the length of the opposite leg divided by the length of the adjacent leg.
Researching the problem in the internet, it is found that for the right triangle in this problem:
- The length of the opposite leg to angle F is of 6.
- The length of the adjacent leg to angle F is of x.
- The length of the hypotenuse is of 11.
Applying the Pythagorean Theorem, we have that:
[tex]6^2 + x^2 = 11^2[/tex]
[tex]36 + x^2 = 121[/tex]
[tex]x^2 = 85[/tex]
[tex]x = \sqrt{85}[/tex]
Considering that the tangent is the length of the opposite leg divided by the length of the adjacent leg, we have that:
[tex]\tan{F} = \frac{6}{\sqrt{85}} \times \frac{\sqrt{85}}{\sqrt{85}} = \frac{6\sqrt{85}}{85}[/tex]
To learn more about tangent, you can take a look at https://brainly.com/question/24680641
