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=√(a^2+b^2) \\ c=√(5^2+5^2) \\ c=√(25+25) \\ c=√(2\cdot25) \\ c=5√(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=(c)/(b) \\ secA=(5√(2))/(5) \\ secA=√(2) \end{gathered}`

It means that correct answer is √2.