SOLUTION: Will you please help. I'm stuck. Solve triangle ABC if C=90 degrees, B=20 degrees, and b=10. Round measures of sides to the nearest tenth and measures of angles to the nearest d

Algebra ->  Trigonometry-basics -> SOLUTION: Will you please help. I'm stuck. Solve triangle ABC if C=90 degrees, B=20 degrees, and b=10. Round measures of sides to the nearest tenth and measures of angles to the nearest d      Log On


   

Question 169392: Will you please help. I'm stuck.
Solve triangle ABC if C=90 degrees, B=20 degrees, and b=10. Round measures of sides to the nearest tenth and measures of angles to the nearest degree. I have to show my work, and don't understand how to do this.
Thank you
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Since it's a triangle you know that,
A%2BB%2BC=180
A%2B90%2B20=180
A=70
I'm assuming that b is the side across from angle B.
Since one of the angle is 90 degrees, it's a right triangle and
a%5E2%2Bb%5E2=c%5E2
Also from trig,
sin%2820%29=b%2Fc
tan%2820%29=a%2Fc
sin%2820%29%2Fcos%2820%29=%28b%2Fc%29%2F%28a%2Fc%29=b%2Fa
tan%2820%29=b%2Fa
a=b%2Ftan%2820%29
a=10%2Ftan%2820%29
a=10%2F0.36397
a=27.47
and from above,
a%5E2%2Bb%5E2=c%5E2
%2827.47%29%5E2%2B10%5E2=c%5E2
754.86%2B100=c%5E2
c%5E2=854.86
c=29.24
Angles to the nearest degree,
A=70
B=20
C=90
Sides to the nearest tenth,
a=27.5
b=10
c=29.2