Question

Find the exact value of tan A in simplest radical form.

Answer 1

Answer:   sqrt(3)

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Work Shown:

The tangent ratio involves the opposite over adjacent.

tan(angle) = opposite/adjacent

tan(A) = BC/AC

tan(A) = sqrt(75)/5

tan(A) = ( 5*sqrt(3) )/5 .... see the section below

tan(A) = sqrt(3)

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sqrt(75) = sqrt(25*3)

sqrt(75) = sqrt(25)*sqrt(3)

sqrt(75) = 5*sqrt(3)