Question

Given the sample triangle below and the conditions a=5,b=5 find sec(A)

Answer 1

The first step to solve this question is to find the measure of the hypotenuse (c) of the triangle using the Pythagorean theorem:

$\begin{gathered} c=\sqrt{a^2+b^2} \\ c=\sqrt{5^2+5^2} \\ c=\sqrt{25+25} \\ c=\sqrt{2\cdot25} \\ c=5\sqrt{2} \end{gathered}$

Now, we have to remember that secant is the ratio of the hypotenuse and the adjacent side to the given angle.

In this case the hypotenuse is c and the adjacent side is b:

$\begin{gathered} secA=\frac{c}{b} \\ secA=\frac{5\sqrt{2}}{5} \\ secA=\sqrt{2} \end{gathered}$

It means that correct answer is √2.