Question

Find the degrees of all the sides

Answer 1

You can use the law of Cosines to solve an SSS triangle.


`cos A = (b^2 + c^2 - a^2)/(2bc)`
a = 13
b = 21
c = 29
Lets find A first:

`cos A = (b^2 + c^2 - a^2)/(2bc)`

`cos A = (21^2 + 29^2 - 13^2)/(2(21)(29))`

`cos A = (441+ 841 - 169)/(1218)`

`cos A = (1113)/(1218)`

`cos A = (53)/(58)`


`A = cos^(-1)((53)/(58)) = 23.96509`

Now lets find B

`cos B = (a^2 + c^2 - b^2)/(2ac)`

`cos B = (13^2 + 29^2 - 21^2)/(2(13)(29))`

`cos B = (169 + 841 - 441)/(754)`

`cos B = (569)/(754)`


`B = cos^(-1)((569)/(754)) = 41.0059`

Since we know A and B we can use
C = 180 - A - B to find C

C = 180 - A - B
C = 180 - 23.96509 - 41.0059
C = 115.0291

A = 23.9650
B = 41.0059
C = 115.0291

Round to nearest tenths.
A = 24.0
B = 41.0
C = 115.0