Respuesta :
Answer:
• A=25.5°
,• B=116.5°
,• b=14.5 units
Explanation:
Given triangle ABC where:
• a = 7
,• c = 10
,• m∠C=38°
(a)First, we find the measure of angle A using the law of sines.
[tex]\frac{\sin A}{a}=\frac{\sin C}{c}[/tex]Substitute the given values:
[tex]\begin{gathered} \frac{\sin A}{7}=\frac{\sin38\degree}{10} \\ \sin A=\frac{\sin(38)\operatorname{\degree}}{10}\times7 \\ A=\arcsin\left(\frac{\sin(38)\operatorname{\degree}}{10}\times7\right) \\ A=25.5\degree \end{gathered}[/tex](b)Next, we find the measure of angle B.
The sum of the measures of angles in a triangle is 180 degrees.
[tex]\begin{gathered} 38\degree+25.5\degree+m\angle B=180\degree \\ m\angle B=180\degree-(38\degree+25.5\degree) \\ m\angle B=116.5\degree \end{gathered}[/tex]The measure of angle B is 116.5 degrees.
(c)Finally, we find the length of b.
[tex]\frac{b}{\sin B}=\frac{c}{\sin C}[/tex]Substitute the given values:
[tex]\begin{gathered} b=\frac{c}{\sin C}\times\sin B \\ =\frac{10}{\sin38\degree}\times\sin116.5\degree \\ =14.5 \end{gathered}[/tex]The length b is 14.5 units.
