Answer:
(a) 27°
Step-by-step explanation:
You want the smallest angle in a triangle with side lengths 7 cm, 12 cm, and 15 cm.
Law of cosines
The law of cosines tells you angle C will satisfy the relation ...
[tex]c^2=a^2+b^2-2ab\cdot \cos(C)\\\\C=\arccos\left(\dfrac{a^2+b^2-c^2}{2ab}\right)=\arccos\left(\dfrac{12^2+15^2-7^2}{2\cdot12\cdot15}\right)\\\\\\C=\arccos\left(\dfrac{320}{360}\right)\approx27.266^\circ[/tex]
The angle opposite the 7 cm side is about 27°, choice A.
