Apply the Pythagorean theorem to determine the length of side b.
`b=sqrt(25^2-20^2)=15`
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:
`tanB=15/20=0.75`
Thus tan(B)=0.75
The definition of cosecant is:
csc A=hypotenuse / opposite leg
The leg opposite to angle A is 20 and the hypotenuse is 25
`cscA=25/20=1.25`
Thus csc(A)=1.25
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:
`cosA=15/25=0.6`
Thus cos(A)=0.6
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