# Find sec B and write as a simplified fraction.

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We can use pythagorean theorem to determine the dimenstion of the hypotenuse.This gives

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

`x^2=1521`

`x=39`

We know that `secB= 1/cosB`

since the cosine of an angle is defined as the ratio of the adjacecent side to the hypotenuse, we get

`cosB = 15/39`

So,

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We can use pythagorean theorem to determine the dimenstion of the hypotenuse.This gives

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

`x^2=1521`

`x=39`

We know that `secB= 1/cosB`

since the cosine of an angle is defined as the ratio of the adjacecent side to the hypotenuse, we get

`cosB = 15/39`

So,

`secB = 1/cosB = 1/(15/39) = 39/15`

Then, if we simplify the fraction by dividing the numerator and denominator by 3, we obtain

`secB = 13/5`

Approved by eNotes Editorial Team

This triangle is a multiple of a 5-12-13 triangle:

The vertical leg is 5x3=15 units long

The horizontal leg is 12x3=36 units long

Therefore the hypotenuse x=13x3=39 units long.

Determine the secant:

secant = 1/cosine     or

secant =` ` hypothenuse/ adjacent leg

`sec B=39/15`

Simplify the fraction by dividing numerator and denominator by 3.

`secB=13/5`

Therefore sec B = 13/5

Approved by eNotes Editorial Team