Question

If the sine of an angle equals to {2}/{5}, then the tangent of the angle could be:

Answer 1

Answer:

If the sine of an angle equals to {2}/{5}, then the tangent of the angle could be:

5. $\frac{2}{\sqrt{21} }$

Step-by-step explanation:

• Imagine a triangle

• The sine of an angle is equal to the length of the opposite leg over the hypotenuse.
• HINT: SOHCAHTOA

To find the adjacent leg (a):

Using the pythagorean theorem: $a^{2} + b^{2} =c^{2}$

- 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:

$a^{2} + 2^{2} =5^{2}$

where a is the adjacent leg of the triangle, solving for a we get:

$a^{2} =5^{2}- 2^{2}$

$a^{2} = 21$

$a = \sqrt{21}$

To find the tangent of the angle:

Since tangent is opposite leg over the adjacent leg:

tan θ = $\frac{2}{\sqrt{21} }$