Answer:
63.5
Step-by-step explanation:
The diagonals of a rhombus bisect opposite angles.
The longer diagonal bisects the 42° angle
The larger angle of the rhombus is 180 - 42 = 138
Let x = the length of the longer diagonal
You know two sides and the included angle of a triangle.
Using the law of cosines we get
[tex]x^{2} = 34^{2} + 34^{2} -2(34)(34) cos 138\\ = 1156 + 1156 - 2312 cos 138\\ = 4030.150837...\\x = \sqrt{4030.150837} = 63.48[/tex][tex]x^{2} = 34^{2} + 34^{2} -2(34)(34)cos 138\\ = 1156 + 1156 - 2312 cos 138\\ = 4030.1508...\\ x = \sqrt{4030.1508} \\ = 63.48[/tex]x^2 = 34^2 + 34^2 - 2(34)(34) cos 138
= 1156 + 1156 - 2312 c0s 138
= 4030.1508...
x = sq rt 4030.1508...
= 63.5
