The given triangle is a right angle triangle.
We would determine the unknown side by applying pythagoras theorem which is expressed as
hypotenuse^2 = opposite side^2 + adjacent side^2
Looking at the triangle, with θ as the reference angle,
hypotenuse = 12
opposite side = 12
adjacent side = unknown side
thus,
adjacent side^2 = 13^2 - 12^2 = 169 - 144 = 25
secθ = 1/cosecθ
To find secθ, we would first find cosecθ
To determine cosecθ, we would apply the cosine trigonometeric ratio.
Cosθ = adjacent side/hypotenuse
Cosθ = 5/13
Since Secθ = 1/cosθ, it means that
secθ = 1/(5/13) = 1 * 13/5
Secθ = 13/5 = 2.6
Sinθ = opposite side/hypotenuse = 12/13
Sinθ = 12/13
Tanθ = opposite side/adjacent side = 12/5
Tanθ = 2.4