Question

In △ABC, m∠A=32°, m∠B=25°, and a=18. Find c to the nearest tenth.

Answer 1

28.5

Explanation:

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Answer 2

28.5

Explanation:

We have been given that in △ABC, m∠A=32°, m∠B=25°, and a=18. We are asked to find the value of c to nearest tenth.

We will use law of sines to solve our given problem.

`\frac{a}{\text{sin}(A)}=\frac{b}{\text{sin}(B)}=\frac{c}{\text{sin}(C)}`, where a, b and c are opposite sides to angle A, B and C.

First of all, we will find measure of angle C using angle sum property.

`m\angle A+m\angle B+m\angle C=180^(\circ)`

`32^(\circ)+25^(\circ)+m\angle C=180^(\circ)`

`57^(\circ)+m\angle C=180^(\circ)`

`57^(\circ)-57^(\circ)+m\angle C=180^(\circ)-57^(\circ)`

`m\angle C=123^(\circ)`

Substituting our values in law of sines, we will get:

`\frac{18}{\text{sin}(32^(\circ))}=\frac{c}{\text{sin}(123^(\circ))}`

Switch sides:

`\frac{c}{\text{sin}(123^(\circ))}=\frac{18}{\text{sin}(32^(\circ))}`

`\frac{c}{\text{sin}(123^(\circ))}*\text{sin}(123^(\circ))=\frac{18}{\text{sin}(32^(\circ))}*\text{sin}(123^(\circ))`

`c=(18)/(0.529919264233)*0.838670567945`

`c=33.9674384664105867*0.838670567945`

`c=28.487490910261`

`c\approx 28.5`

Therefore, the value of c is 28.5 to the nearest tenth.