Question

a right triangle has acute angle theta and cos theta = 2/5. what are the other 5 trigonometric ratios of theta?

Answer 1

The ratio for cosine is adjacent/hypotenuse. You can remember the ratios by thinking of SOH CAH TOA. (sin = opp/hyp, cos = adj/hyp, tan = opp/adj).

Since the cosine is adjacent over hypotenuse, and the cos theta in the triangle is 2/5, you now know what the adjacent and hypotenuse are. Then use the pythagorean theorem to find the last side. a^2 + b^2 = c^2. A is the adjacent side, and c is the hypotenuse. See if you can find b.

Answer 2

b = 5.4?

Answer 3

You can find the rest of the things

Answer 4

Close. Did you plug in for a and c?

\[2^2+b^2=5^2\]\[4+b^2=25\]\[b^2=21\]\[\sqrt{21}=4.58\]

Answer 5

I have no idea what i did lol I've been doing math constantly for 5 days straight, which is why I get confused and lost so easily. Sorry, keep going please.

Answer 6

Lol I know what you mean. It's ok. So now that you have b=4.58, that is the opposite of the theta angle.

The 6 ratios are cosine, sine, tangent, secant, cosecant, and cotangent. You already have cosine. Remember SOH CAH TOA for sine and tangent.

Secant(sec) is the reciprocal of cosine, so instead of adj/hyp, it is hyp/adjacent.

Cosecant(csc) is the reciprocal of sine, so it is hyp/opp.

Cotangent is the reciprocal of tangent, so adj/opp.

Answer 7

So I just plug in all my values and write them as fractions?

Answer 8

Yes. Remember that the sides are to the theta angle. So the hypotenuse is the long side(5), the adjacent side is 2, and the opposite is 4.58.

Answer 9

Sometimes it's easier to draw it out so you don't get mixed up. That's what I do.

Answer 10

Thank you! While I type all that out, can you help me with this one?

http://puu.sh/3eb1A.png

Answer 11

Your welcome! Typing out math sucks.. Idk why teachers make us do that :/

Answer 12

i don't get it either. /

Answer 13

cos40º = adjacent side / hypotenuse
cos40º = 8000/d
d = 8000/cos40º
The question give the value of cos40º :]

Answer 14

Ok so since you already have 2 of the angles, just subtract them both from 180 to find the last angle. 180-90-40=50.

You'll probably want to do the law of sines on this one. Basically the law of sines is a ratio of the sine of the angle over its side is equal to the same ratio of another side and angle...

\[\frac{ \sin 50^{o} }{ 8000 }=\frac{ \sin 90^{o} }{ d }\]
After that you cross multiply. So \[\sin50^{o}d=\sin90^{o}(8000)\]Use a graphing calculator to find simplify. If you do sin 50 degrees, make sure to put the degree sine on the calculator. Press 2nd, angle, and 1 to put the degree sign. Sin90deg is 1 because of the unit circle. So simplify and solve for d.

Answer 15

Zair's way works too. It's probably simpler lol but I do it this way out of habit because I always get mixed up with the law of cosine.

Answer 16

D = 6160, but that doesnt make sense because D is longer than the side with 8000 ft.

Answer 17

How ddi you get 6160?

Answer 18

cos40º = 0.77
Do 8000/0.77 = 10389,61

Answer 19

I think zair's way is easier. Sorry for confusing you.

Answer 20

i did it backwards. duh. omg. lol thank you

Answer 21

No problem

Answer 22

LAST ONE:

http://puu.sh/3ebAa.png

Answer 23

angle a = 51

Answer 24

How did you get angle a? 180-90-31=59.

Answer 25

oops, read it from my paper wrong. lol i'm all over the place today