Respuesta :
Answer:
28.5
Step-by-step 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.
[tex]\frac{a}{\text{sin}(A)}=\frac{b}{\text{sin}(B)}=\frac{c}{\text{sin}(C)}[/tex], 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.
[tex]m\angle A+m\angle B+m\angle C=180^{\circ}[/tex]
[tex]32^{\circ}+25^{\circ}+m\angle C=180^{\circ}[/tex]
[tex]57^{\circ}+m\angle C=180^{\circ}[/tex]
[tex]57^{\circ}-57^{\circ}+m\angle C=180^{\circ}-57^{\circ}[/tex]
[tex]m\angle C=123^{\circ}[/tex]
Substituting our values in law of sines, we will get:
[tex]\frac{18}{\text{sin}(32^{\circ})}=\frac{c}{\text{sin}(123^{\circ})}[/tex]
Switch sides:
[tex]\frac{c}{\text{sin}(123^{\circ})}=\frac{18}{\text{sin}(32^{\circ})}[/tex]
[tex]\frac{c}{\text{sin}(123^{\circ})}*\text{sin}(123^{\circ})=\frac{18}{\text{sin}(32^{\circ})}*\text{sin}(123^{\circ})[/tex]
[tex]c=\frac{18}{0.529919264233}*0.838670567945[/tex]
[tex]c=33.9674384664105867*0.838670567945[/tex]
[tex]c=28.487490910261[/tex]
[tex]c\approx 28.5[/tex]
Therefore, the value of c is 28.5 to the nearest tenth.
