Question

Solve the triangle. B = 36°, a = 38, c = 17

Answer 1

hmmm what "solve" means?

Answer 2

find b, A, and C
I have found "b" b=26.2

Answer 3

the answer options are:

b ≈ 41.3, C ≈ 22.3, A ≈ 121.7

b ≈ 41.3, C ≈ 26.3, A ≈ 117.7

b ≈ 26.2, C ≈ 118.7, A ≈ 25.3

b ≈ 26.2, C ≈ 22.3, A ≈ 121.7

Answer 4

I assume you've covered the Law of Cosines?

Answer 5

and then I used the Law of Cosine to find "A," but I get =189.40 which isn't a choice

Answer 6

hmm what did you get for side "b"?

Answer 7

For side "b" I got 26.2... by using the equatoin b^2 = a^2 + c^2 - 2ac(CosB)

Answer 8

ok I got 26.2 as well

Answer 9

now use sin formula to find the angle A or angle C or both.

Answer 10

\(\bf \textit{Law of Cosines}\\ \quad \\
a^2 = {\color{blue}{ b}}^2+{\color{red}{ c}}^2-(2{\color{blue}{ b}}{\color{red}{ c}})cos(A)\implies
cos(A)=\cfrac{{\color{blue}{ b}}^2+{\color{red}{ c}}^2-a^2}{2{\color{blue}{ b}}{\color{red}{ c}}}\\ \quad \\
\measuredangle A = cos^{-1}\left(\cfrac{{\color{blue}{ b}}^2+{\color{red}{ c}}^2-a^2}{2{\color{blue}{ b}}{\color{red}{ c}}}\right)\)

Answer 11

\[\frac{ 26.2 }{ \sin 36 }=\frac{ 38 }{ \sin A }=\frac{ 17 }{ \sin C }\]

Answer 12

@surjithayer and @jdoe0001 Thank you both so much! This is my first time on here and I didn't think everyone would be so nice! :)

Answer 13

yw