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Could someone help me with this question (Trigonometry)?

Could someone help me with this question (Trigonometry)?-example-1
User MTilsted
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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

User Syed Tariq
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