Answer:
Step-by-step explanation:
I don't know where you are in your class, or even what chapter you are in, but I solved this using a right triangle.
We don't need to know the angles, just the sides.
c is the hypotenuse, the line at a tilt
b is the adjacent line, directly below c
a is the opposite line
c = 13
a= 12
b = ?
In order to find b, we use the Pythagorean Theorem, [tex]a^{2} + b^{2} = c^{2}[/tex], but we need to rearrange the problem to where we are solving for b instead of c, [tex]b^{2} = a^{2} + c^{2}[/tex]
[tex]b^{2} = (12)^{2} + (13)^{2}\\b^{2} = 144 + 169\\b^{2} = 313 \\\sqrt{b^{2} } = \sqrt{313}\\ b = 17.69[/tex]
So, b = 17.69
Now, we need to evaluate each of the trig. functions:
[tex]sin = \frac{opposite}{hypotenuse} = \frac{12}{13} \\csc = \frac{hypotenuse}{opposite} = \frac{13}{12} \\cos = \frac{adjacent}{hypotenuse} = \frac{17.69}{13} \\sec = \frac{hypotenuse}{adjacent} = \frac{13}{17.69}\\tan = \frac{opposite}{adjacent} = \frac{12}{17.69}\\cot = \frac{adjacent}{opposite} = \frac{17.69}{12}[/tex]
So, there is your answers, hope that is what you are looking for.
