Answer:
B= 50.35°
C=91.65°
c= 12.77
Step-by-step explanation:
Given:
A = 38°
b= 10 and a=8.
Required:
angles B and C, and sides c.
By using the rule for law of sines
[tex]sin B=b\frac{sinA}{a} = \frac{(10)(0.62)}{8}[/tex] => 0.77
B= [tex]sin^-^1[/tex](0.77) => 50.35°
For angle C:
angle C= 180 - A - B => 180 - 38 - 50.35
=91.65°
For side c:
c=[tex]a(\frac{sinC}{sinA} )[/tex] => 8([tex]\frac{0.99}{0.62}[/tex])
c= 12.77
Answer:
A=38 degrees, B=50 degrees, C=92 degrees
a=8, b=10, c=13
Step-by-step explanation:
Given a triangle where: A=38°, b= 10, and a=8.
Using Law of Sines
[tex]\dfrac{a}{sin A} =\dfrac{b}{sin B} \\\dfrac{8}{sin 38} =\dfrac{10}{sin B} \\$Cross multiply\\8 X sin B=10 X Sin 38\\Sin B=(10 X sin 38)\div 8\\B=arcsin[(10 X sin 38)\div 8]\\B\approx50^\circ[/tex]
[tex]\angle A+\angle B+\angle C=180^\circ($Sum of angles in a triangle)\\38+50+\angle C=180^\circ\\\angle C=180-88\\\angle C=92^\circ[/tex]
[tex]\dfrac{a}{sin A} =\dfrac{c}{sin C} \\\dfrac{8}{sin 38} =\dfrac{c}{sin 92} \\$Cross multiply\\8 X sin 92=c X Sin 38\\c=(8 X sin 92)\div sin38\\c\approx13[/tex]
