Answer:
If the sine of an angle equals to {2}/{5}, then the tangent of the angle could be:
5. [tex]\frac{2}{\sqrt{21} }[/tex]
Step-by-step explanation:
To find the adjacent leg (a):
Using the pythagorean theorem: [tex]a^{2} + b^{2} =c^{2}[/tex]
- a and b are the lenght of the sides and c is the hypotenuse
we know one side and the hypotenuse. Therefore plugging into the formula we get:
[tex]a^{2} + 2^{2} =5^{2}[/tex]
where a is the adjacent leg of the triangle, solving for a we get:
[tex]a^{2} =5^{2}- 2^{2}[/tex]
[tex]a^{2} = 21[/tex]
[tex]a = \sqrt{21}[/tex]
To find the tangent of the angle:
Since tangent is opposite leg over the adjacent leg:
tan θ = [tex]\frac{2}{\sqrt{21} }[/tex]
