Find tan of angle B, csc of angle A, and cos of angle A.

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flbyrne | (Level 3) Assistant Educator

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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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