Find the cosine of an acute angle if its sine is 12/13 find its tangent.

It is known that the squares of sine and cosine add up to one:

cos2α + sin2α = 1.

Means:

cos2α = 1 – sin2α = 1 – (12/13) ^ 2 = 1 – 144/169 = (169 – 144) / 169 = 25/169.

Since the coal is sharp, its cosine and sine take positive values, therefore:

cos α = √ (25/169) = 5/13.

The tangent of the angle is equal to the ratio of sine to cosine:

tg α = sin α / cos α = (12/13) / (5/13) = 12/5 = 2.4.