To find: All solutions for triangle A=107.2∘,a=17.2,c=12.2 . If no solutions exist, write none . Round to the nearest tenth

Expert Solution & Answer

Answer to Problem 25E

∠C=42.7∘,∠B=30.1∘,b=9

Explanation of Solution

Given information: A=107.2∘,a=17.2,c=12.2

Calculation:

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition, Chapter 5.7, Problem 25E

Case II, since an angle is greater or equal to a right angle

The side opposite to the greatest angle is longer than the other given side,

17.2≥12.2

There is one solution.

With the sine law we find the angle for pair c − C

Using the law of sines

asinA=csinCsinC=c×sinAasinC=12.2sin107.217.2C=sin−1(12.2sin107.217.2)C≈42.65491∘≈42.7∘B≈180∘−(107.2∘+42.7∘)=30.1∘

Having two angles (A and C), we find the third, B and with the law of sines, find b .

bsinB=asinAb=17.2×sin30.1∘sin107.2∘=9.04206

Round off,

Thus,

∠C=42.7∘,∠B=30.1∘,b=9

Chapter 5.7, Problem 24E

Chapter 5.7, Problem 26E

Chapter 5 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

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