Apply the Pythagorean theorem to determine the length of side b.
Another way of finding side b is by noting that this triangle is a multiple of a 3-4-5 right triangle, in which the legs are 3 and 4 and the hypotenuse is 5. In this case the legs are 3x5=15, 4x5=20 and the hypotenuse is 5x5=-25.
The definition of tangent is:
tan B=opposite leg / adjacent leg
The leg opposite to angle B has a length of b=15 and the adjacent leg has a length of 20. Therefore:
The definition of cosecant is:
csc A=hypotenuse / opposite leg
The leg opposite to angle A is 20 and the hypotenuse is 25
The definition of cosine is:
cos A= adjacent leg / hypotenuse
The leg adjacent to angle A is b=15 and the hypotenuse is 25, therefore: