Question

GEOMETRY HELP PLEASE(:.
Given the triangle below, what is sec ∡B?

http://learn.flvs.net/webdav/assessment_images/educator_geometry_v14/pool_Geom_3641_0403_03/image0034e2ec0b0.gif

Right triangle ABC with AC measuring 4 and BC measuring 7.

Answer 1

Remember. \[\sec B = \frac{hyp.}{adj.}\]

Answer 2

We have to find Adjacent since it's not there right?

Answer 3

Ok. Since we have two unknowns, we have to do something else first.

Answer 4

First use \[\sin B = \frac{4}{7}\]to figure out what B is.

Answer 5

Can you do that?

Answer 6

I did it but I got 34 something which I'm sure isn't the answer. Just curious, can't we just do the Pythagorean theorem here?

Answer 7

You can, but I find this easier because you can just plug it into a calculator afterwards.

Answer 8

Okay so 34.8490 isn't the answer right?

Answer 9

34.8499*

Answer 10

34.8499 is the measure of \(\angle B\). Now just plug 1/cos34.8499 in order to get \(\sec B\) :)

Answer 11

1.21854352387946?

Answer 12

Yup :)

Answer 13

Thanks(: By the way do you know the formulas for the other two? Not sin tan or cos but the other 2 :P

Answer 14

\[\sec ß = \frac{1}{\cos ß} \space or \space \frac{hyp.}{adj.}\]\[\csc ß = \frac{1}{\sin ß} \space or \space \frac{hyp.}{opp.}\]\[\cot ß = \frac{1}{\tan ß} \space or \space \frac{adj.}{opp.}\]

Answer 15

Okie dokie, I wrote that down. Thank you so much(:.

Answer 16

http://www.purplemath.com/modules/basirati.htm

YES. you can do the Pythagorean theorem. That's how you would start anyway if you want to show a step-by-step solution. \[\sec \theta = 1/\cos\]
\[\sec \theta=1/\left( 4/7 \right) = 7/4\]

Answer 17

@panlac01 sec is 1/cos. We don't have the adj. side for that.
@AmauryP You can use Pythagorean THeorem I guess and then use the sec ratio and solve that to get sec B

Answer 18

I understand it either way, thanks guys(:.

Answer 19

the adjacent side is 4