Question

Solve the triangle.

B = 36°, a = 41, c = 17

Answer 1

use a2+b2=c2

Answer 2

wait i think i am wrong

Answer 3

have you covered the "Law of Cosines" yet?

Answer 4

You can't use the Pythagorean Theorem here because we don't know that this is a right-angled triangle. We have 2 sides and an angle, so I would use the Cosine Law.

Answer 5

yea i was thinking that to @matt101

Answer 6

have you fainted yet? =) did you recover yet?

Answer 7

well... I guess if you haven't... wouldn't be able to answer anyhow

Answer 8

OS is lagging sorry. But yes I have covered the Laws of Cosine.

Answer 9

\(\bf \textit{Law of Cosines}\\ \quad \\
b^2 = {\color{blue}{ a}}^2+{\color{red}{ c}}^2-(2{\color{blue}{ a}}{\color{red}{ c}})cos(B)\implies

b = \sqrt{{\color{blue}{ a}}^2+{\color{red}{ c}}^2-(2{\color{blue}{ a}}{\color{red}{ c}})cos(B)}\)

so that'd get you side "b"

then you'd just need to find the other 2 angles

Answer 10

Would it look something like this
\[b^2=41^2+17^2-2(41)(17)CosB\]

Answer 11

yeap

Answer 12

so then once you have side "b",

then you'd need to find the other angles

since the sum of all internal angles in a triangle is 180
if you just find one of the other angles, you can pretty much get the other from 180-(sum of the other two angles)

Answer 13

So then it would be \[b^2=1681+289-1394CosB\]\[b^2=1970-1394CosB\]\[b^2=576CosB\]Do I find the square root of 576?

Answer 14

yeap

Answer 15

So b is 24? That isn't one of my answer choices. Did I do something wrong?

Answer 16

https://www.google.com/search?client=opera&q=sqrt(41%5E2%2B17%5E2-(2*41*17*cos(36+degrees)))&sourceid=opera&ie=utf-8&oe=utf-8&channel=suggest&gws_rd=ssl

Answer 17

so... once you found "b"
you have all 3 sides, "a", "b" and "c" so, to find another angle just solve for cosine, that is \(\bf c^2=a^2+b^2-2ab\cdot cos(C)\implies c^2-a^2-b^2=-2ab\cdot cos(C)
\\ \quad \\
\cfrac{c^2-a^2-b^2}{-2ab}= cos(C)\implies cos^{-1}\left[\cfrac{c^2-a^2-b^2}{-2ab}\right]=cos^{-1}[cos(C)]
\\ \quad \\
cos^{-1}\left[\cfrac{{\color{red}{ c}}^2-{\color{blue}{ a}}^2-b^2}{-2{\color{blue}{ a}}b}\right]=\measuredangle C\)

Answer 18

and angle A as you'd know, it'll be 180 - ( B+C)

Answer 19

So C would be 20?

Answer 20

20.14 approximately, in degrees, yes

Answer 21

Awesome! So then A would be 124, if my calculations are correct.

Answer 22

yeap

Answer 23

Thank you for your help. You made this so easy to understand! :)

Answer 24

yw