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91Ó°ÊÓ

Solve each triangle.

b=1c=3,A=80°

Short Answer

Expert verified

The solution isa≈3,B≈19.6°,C≈80.4°.

Step by step solution

01

Step 1. Given information 

b=1c=3,A=80°

02

Step 2. Calculation 

Use Law of Cosines -

a2=b2+c2-2bccosA

=1+9-2×1×3cos80°

localid="1646858065045" ≈10-6×0.17

localid="1646891425407" a≈3

For C:

localid="1646858918647" c2=a2+b2-2abcosC

localid="1646891487034" cosC=a2+b2-c22ab≈9+1-92×3×1≈16

localid="1646891543751" C≈cos-116≈80.4°

Since we know Aand C,

B≈180°-80°-80.4°≈19.6°

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