Use the Law of Cosines to solve the triangles. Round lengths to the nearest tenth and angle measures to the nearest degree. a=4, b=6, c=9 a=4, b=7, c=6

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Use the Law of Cosines to solve the triangles. Round lengths to the nearest tenth and angle measures to the nearest degree.  a=4, b=6, c=9  a=4, b=7, c=6

Sue Leahy · Accepted Answer

Step 1  For a triangle with sides a, b, c and angles A, B, C the law of consines is defined as:  c2=a2+b2−2ab×cos⁡(C)  ⇒cos⁡(C)=a2+b2−c22ab  ⇒cos⁡(C)=42+62−922×4×6  ⇒cos⁡(C)=−0.60416  ⇒C=cos−1(−0.60416) (Because cos⁡(C) is negative, C is an obtuse angle.)  ⇒∠C=127.17∘≈127∘  Step 2  Now we will use law ofsines to find angle A.  sin⁡(A)a=sin⁡(C)c  ⇒sin⁡(A)=4sin⁡(127∘)9  ⇒sin⁡(A)=0.35494  ⇒A=arcsin⁡(0.35494)  ⇒∠A=20.7898∘≈21∘  Now ∠B−180∘−∠A−∠C  =180∘−127∘−21∘  ∠B=32∘  Step 3  2nd Triangle: a=4, b=7, c=6  First we will find angle B using law of cosines.  b2=a2+c2−2ac×cos⁡(B)  ⇒cos⁡(B)=a2+c2−b22ac  ⇒cos⁡(B)=42+62−722×4×6  ⇒cos⁡(B)=0.0625  ⇒B=cos−1(0.0625)  ⇒∠B=86.4164∘≈86∘  Step 4  Now we will find A by using law of sines.  asin⁡(A)=bsin⁡(B)

Use the Law of Cosines to solve the triangles. Round

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