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A triangle has sides of length 7 cm, 12 cm, and 15 cm.
What is the measure of the angle opposite the side that is 7 cm long? Round to the nearest degree.
O 27°
O 42°
O63
077°
​

Sagot :

Sqdancefanidn

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.

 

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