Step-by-step explanation:
We know that:
[tex] \tan( \alpha ) = \frac{15.5}{25} = 0.62 [/tex]
So you need to find an angle α that its tangent is equal to 0.62. This is not something easily done on your own. So I suggest you to search for tangent tables or look it up online.
I searched it and found that:
[tex] \tan(31.8 \: deg) = 0.62[/tex]
You can go a step ahead and find the sine and cosine of this angle approximately.
We have that
[tex] \tan( \alpha ) = \frac{ \cos( \alpha ) }{ \sin( \alpha ) } \\ which \: means \\ \tan( \alpha ) \times \sin( \alpha ) = \cos( \alpha ) [/tex]
Also we know the trigononetric identity that is true for all angles:
[tex] { \sin( \alpha ) }^{2} + { \cos( \alpha ) }^{2} = 1[/tex]
So we have that:
[tex] \cos( \alpha ) = 0.62 \times \sin( \alpha ) [/tex]
Which leads to:
[tex] { \sin( \alpha ) }^{2} + { {(0.062 )}^{2} \sin( \alpha ) }^{2} = 1 \\ \ { \sin( \alpha ) }^{2} (1 + {0.062}^{2} ) = 1 \\ (1. 3844) \ { \sin( \alpha ) }^{2} = 1 \\ \ | \sin( \alpha ) | = \sqrt{ \frac{1}{1.3844} } \\ | \sin( \alpha ) | = 0.849902691712[/tex]
Which means that:
[tex] | \cos( \alpha ) | = \sqrt{1 - { \sin( \alpha ) }^{2} } \\ | \cos( \alpha ) | = \sqrt{1 - { \sqrt{ \frac{1}{1.3844} } }^{2} } \\ | \cos( \alpha ) | = \sqrt{1 - \frac{1 }{1.3844} } \\ | \cos( \alpha ) | = 0.526939668861[/tex]
These are numbers hard to calculate but its easier to do that finding the angle of a respective tangent.
