Answer:
B=77° 44'
a=6.649 cm
c=1.479 cm
Step-by-step explanation:
Given
A = 12° 54'=12.54°,
C=90°
b = 6.812 cm
Required:
B = ______ °_________ '=?
a = _________cm
c = _________cm
Solution:
B = ______ °_________ '=?
As we know that sum of angles in a triangle is 180
sum A+B+C=180
12.54+B+90=180
B+102.54=180
subtracting 102.54 from both sides, we get
B=77.46°
B = 77 ° 44 '
a = _________cm
As we know that
[tex]cos\theta=base/hypotenous\\\\cos\theta=a/b\\\\\theta=12.54\\\\cos(12.54)=a/6.812\\\\a=cos(12.54)*6.812\\\\a=0.976*6.812\\\\a=6.649cm[/tex]
c = _________cm=?
As we know that
[tex]sin\theta=perpendicular/hypotenous\\\\sin\theta=b/c\\\\\theta=12.54\\\\sin(12.54)=6.812/c\\\\c=sin(12.54)*6.812\\\\c=0.217*6.812\\\\c=1.479cm[/tex]
