Find sec B and write as a simplified fraction.
We can use pythagorean theorem to determine the dimenstion of the hypotenuse.This gives
`x^2 = 15^2+36^2`
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` = adjacent/hypotenuse
`cosB = 15/39`
`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`
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
Simplify the fraction by dividing numerator and denominator by 3.
Therefore sec B = 13/5