Write the ratios for sin A and cos A. The diagram is not to scale
A-B is 12
B-C is 5
C-A is 13
and angle b is a right angle
To find the ratios for sin A and cos A, we first need to find the lengths of all sides in the right triangle ABC.
Using the Pythagorean theorem (a^2 + b^2 = c^2), we can find the length of side AB:
AB = √(BC^2 + AC^2) = √(5^2 + 13^2) = √(25 + 169) = √194 ≈ 13.93
Now, we can find the ratio for sin A:
sin A = opposite/hypotenuse = BC/AB = 5/13.93
And the ratio for cos A:
cos A = adjacent/hypotenuse = AC/AB = 13/13.93
Therefore, the ratios for sin A and cos A are:
sin A ≈ 0.358
cos A ≈ 0.932