Question

Given the right triangle find the value of sec(90 degree - theta) when a= 12, b= 5, c= 13

Answer 1

Use the next trigonometric identities:

$\begin{gathered} \sec (90º-\theta)=\frac{1}{\cos (90º-\theta)} \\ \\ \cos (90º-\theta)=\sin \theta \end{gathered}$

Then, the sec(90º - θ) is:

$\sec (90º-\theta)=\frac{1}{\sin \theta}$

The sin(θ) is:

$\sin \theta=\frac{opposite}{hypotenuse}=\frac{5}{13}$

Then:

$\sec (90º-\theta)=\frac{1}{\frac{5}{13}}=\frac{13}{5}$

Then, the sec(90º - θ) is 13/5