Question

Could someone help me with this question (Trigonometry)?

Answer 1

Answer: Choice C)
`\displaystyle (√(5))/(2)`

Work Shown

We'll need to use the pythagorean theorem to find the hypotenuse.

`a^2+b^2 = c^2\\\\c = √(a^2+b^2)\\\\x = √(2^2+4^2)\\\\x = √(20)\\\\x = √(4*5)\\\\x = √(4)*√(5)\\\\x = 2√(5)\\\\`

The hypotenuse is exactly
`2√(5)` units long.

Then we divide the hypotenuse over adjacent to get secant. Recall that secant is the reciprocal of cosine.

`\sec(\text{angle}) = \frac{\text{hypotenuse}}{\text{adjacent}}\\\\\sec(\theta) = (2√(5))/(4)\\\\\sec(\theta) = (√(5))/(2)\\\\`

This leads us to answer choice C