Find cot A and write as a simplified fraction. Find cos A and write as a simplified fraction.

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Find cot A and cos A.

First find the value of x, the hypotenuse.  Use the pythagorean theorem.

`15^2 + 36^2 = x^2`

` ` `x^2 = 1521`

`x = 39`

The cosine of angle is the ratio of the adjacent side to the angle to the hypotenuse.

`cos A = 36/39`

`cos A = 12/13`

The cotangent of an angle is the reciprocal of the tangent ratio.

The tan = `(opp)/(adj)`

Therefore, `cot A = (adj)/(opp)`

`cotA = 36/15`

` ``cot A = 12/5`

The solution is cos A = `12/13` and cot A = `12/5` .

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