Question

What is sec∅ of the following triangle?

Answer 1

$sec(\theta) = \frac{1}{ \cos(\theta) } \\ \cos(\theta) = \frac{adj}{hyp}, \: \: \sec(\theta) = \frac{hyp}{adj}$

Using the Pythagoras theorem,

${hyp}^{2} = {opp}^{2} + {adj}^{2} \\ {hyp}^{2} = {7}^{2} + {24}^{2} \\ {hyp}^{2} = 49 + 576 \\ {hyp}^{2} = 625 \\ hyp = \sqrt{625} \\ hyp = 25$

Plugging in our values,

$\sec(\theta) = \frac{hyp}{adj} \\ \sec(\theta) = \frac{25}{7}$

So the last option is the correct one.

Answer 2

Answer:

$\displaystyle \sec( \theta) = \frac{25}{7}$

Step-by-step explanation:

remember that,

$\displaystyle \sec( \theta) = \frac{hypo}{adj}$

since we aren't given hypo we can consider Pythagoras theorem given by

$\displaystyle {a}^{2} + {b}^{2} = {c}^{2}$

$\displaystyle \implies c = \sqrt{ {a}^{2} + {b}^{2} }$

substitute the value of a and b:

$\displaystyle c = \sqrt{ {7}^{2} + {24}^{2} }$

simplify squares:

$\displaystyle c = \sqrt{49 + 576}$

simplify addition:

$\displaystyle c = \sqrt{625}$

simplify square root:

$\displaystyle c = 25$

with respect to $\theta$ adj is 7 and hypo is 25 thus

substitute:

$\displaystyle \sec( \theta) = \frac{25}{7}$

and we are done!