Unknown Side
For the triangle figure shown, what is the length of the third side?
Expand Hint
Law of Cosines:
$$$c^2=a^2+b^2-2ab\:cos\:C$$$
Hint 2
For oblique (non-right) triangles, use the Law of Cosines to determine unknown sides:
$$$a^2=b^2+c^2-2bc\:cos\:A$$$
$$$b^2=a^2+c^2-2ac\:cos\:B$$$
$$$c^2=a^2+b^2-2ab\:cos\:C$$$
Thus, to find side
$$c$$
:
$$$c^2=a^2+b^2-2ab\:cos\:C$$$
$$$c^2=(21)^2+(15)^2-2(21)(15)\:cos\:28^{\circ}$$$
$$$c^2=441+225-(630)(0.8829)$$$
$$$c=\sqrt{666-556.26}=\sqrt{109.74}=10.5$$$
10.5
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