Trig. Law of Sines and Cosines

[ashleebrook]

I have answers for these problems, but I wanted to check if I had them right because I wasnt sure on some of them....Thanks.
Solve the triangle:
1. a=4, b=8, alpha=30 deg.
answer- beta=90 deg., gamma=60 deg., c=7
2. a=5, b=7, alpha=30 deg.
answer- beta=44 deg., gamma=106 deg., c=10
3. a=3, b=8, alpha=30 deg.
and this one I am doing something completely wrong because I cant find out the first answer...so I do not have an answer for it yet
4. alpha=53 deg., gamma=105 deg., b=42
answer- beta=22 deg., a=108, c=90
5. alpha= 65 deg., b=103, c=53
answer- a=155, gamma=25 deg., beta=90 deg.
6. a=43, b=48, c=53
answer- gamma=71 deg., alpha=50 deg., beta=59 deg.


this isn't a homework problem but something he told us about and I would like to know...how does the law of cosines relate to the Pythagorean theorem? if anyone knows that.

[HallsofIvy]

" have answers for these problems, but I wanted to check if I had them right because I wasnt sure on some of them....Thanks.
Solve the triangle:
1. a=4, b=8, alpha=30 deg.
answer- beta=90 deg., gamma=60 deg., c=7"
Since you are saying beta= 90 degrees, you are claiming this is a right triangle with hypotenuse of length 8: but 4^2+ 7^2= 65 not 8^2= 64. Did you round of to the nearest whole number? Why?

"2. a=5, b=7, alpha=30 deg.
answer- beta=44 deg., gamma=106 deg., c=10"
Okay, except again you appear to be rounding everything to the nearest integer.

"3. a=3, b=8, alpha=30 deg.
and this one I am doing something completely wrong because I cant find out the first answer...so I do not have an answer for it yet"
I don't see how this is at all different from the first two! sin(beta)/8= sin(30)/3= 1/6 so sin(beta)= 8/6= 4/3. Oh! there is no such triangle!

"4. alpha=53 deg., gamma=105 deg., b=42
answer- beta=22 deg., a=108, c=90
5. alpha= 65 deg., b=103, c=53
answer- a=155, gamma=25 deg., beta=90 deg.
6. a=43, b=48, c=53
answer- gamma=71 deg., alpha=50 deg., beta=59 deg."

Only objection is what I said before. Were you told to round everything to the nearest integer?