Hello!
The answer is:
[tex]Sin(u)=0.86\\Cos(u)=0.50\\Tan(u)=1.73[/tex]
Why?
Since it's a right triangle, and we have the adjacent and opposite sides size ([tex]\sqrt{37}[/tex]), we can solve it using following the next steps:
Tan(u),
We can find the tangent using the following formula:
[tex]tan(u)=\frac{OppositeSide}{AdjacentSide}= \frac{\sqrt{111} }{\sqrt{37}}=\frac{10.54}{6.08}\\tan(u)=1.73[/tex]
Sin(u),
To find the sin(u) we need first to find the hypotenuse of the triangle using the Pythagorean Theorem, so:
[tex]c=\sqrt{a^{2}+b^{2}}[/tex]
Where:
[tex]c=hypotenuse\\a=FirstTriangleSide\\b=SecondTriangleSide[/tex]
Substituting we have:
[tex]hypotenuse=\sqrt{\sqrt{37}^{2}+\sqrt{111}^{2}}[/tex]
[tex]hypotenuse=\sqrt{37+111}=\sqrt{148}=12.17[/tex]
Then, we can calculate the sin(u) using the following formula:
[tex]Sin(u)\frac{OppositeSide}{Hypotenuse}=\frac{\sqrt{111} }{12.17}=0.86[/tex]
Finally, we can calculate the cos(u) by using the following formula:
Cos(u),
[tex]cos(u)=\frac{AdjacentSide}{Hypotenuse}=\frac{\sqrt{37} }{12.17}=0.50[/tex]
Hence,
We have that:
[tex]Sin(u)=0.86\\Cos(u)=0.50\\Tan(u)=1.73[/tex]
Have a nice day!
