Find csc B and write as a simplified fraction.

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Find `csc /_B` and write as a simplified fraction.

First, the csc, or cosecant is the reciprocal of the sine function.

The sine of an angle given a right triangle is the ratio of the side opposite the angle to the hypotenuse.

`sin B = 36/x`

`csc B = x/36`

In order to find x, use the pythagorean theorem: `a^2+b^2 = c^2.`

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

`x =sqrt(36^2+15^2) = 39`

`csc B = 39/36 = 13/12`

The csc B is `13/12.`

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