Question

2 part question

Answer 1

1 I: set up sin(theta) = opposite/hypotenuse and solve for b

Answer 2

sin(25)=a/12

Answer 3

good but keep in mind we are using the variable b not a

so sin(25) = b/12

Answer 4

b=5.07

Answer 5

good

then for part II you can simply use the pythagorean theorem to find (a)

Answer 6

a^2+b^2=c^2
a^2=5.07^2+12^2
a=13.08

Answer 7

check your signs carefully

a^2+b^2=c^2

therefore a^2 = c^2 - b^2

Answer 8

the way you have written it, you have

a^2=5.07^2+12^2

which implies that
a^2 = b^2 + c^2
which is not true

Answer 9

you need to solve a^2 + b^2 = c^2 for a^2 which gives us

a^2 = c^2 - b^2

then plug in c and b to get a

Answer 10

a^2 = c^2 - b^2
a^2 = 12^2 - 5.07^2
a=10.88

Answer 11

for part II

Answer 12

I rounded it off

Answer 13

good

Answer 14

any attempts on part I? like it says just use law of cosines