SOLUTION: Solve the triangle. (Round your answers to one decimal place.) a = 4.62 ft, b = 3.54 ft, c = 5.87 ft A= ° B= ° C = °

Algebra ->  Triangles -> SOLUTION: Solve the triangle. (Round your answers to one decimal place.) a = 4.62 ft, b = 3.54 ft, c = 5.87 ft A= ° B= ° C = °       Log On


   

Question 1136158: Solve the triangle. (Round your answers to one decimal place.)
a = 4.62 ft, b = 3.54 ft, c = 5.87 ft
A= °
B= °
C = °
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
4.62+ ft, b+=+3.54+ft, and c+=+5.87+ft,
to find :
A= °
B= °
C+= °

use Law of Cosines:
a%5E2+=+b%5E2+%2B+c%5E2+-2bc+%2Acos%28+A%29...plug in given data
4.62%5E2+=+3.54%5E2+%2B+5.87%5E2+-2%2A3.54%2A5.87+%2Acos%28+A%29
21.3444+=+12.5316+%2B+34.4569+-41.5596+%2Acos%28+A%29
21.3444+-12.5316+-+34.4569=+-41.5596+%2Acos%28+A%29
-25.6441=+-41.5596+%2Acos%28+A%29
41.5596+%2Acos%28+A%29=25.6441
+cos%28+A%29=25.6441%2F41.5596
+cos%28+A%29=0.61704395614972232649
+A=cos%5E-1%28+0.61704395614972232649%29
+A=51.899411629220270907°
+A=51.9°

c%5E2+=+a%5E2+%2B+b%5E2+-2ab+%2Acos%28+C%29...plug in given data
5.87%5E2+=+4.62%5E2+%2B+3.54%5E2+-2%2A4.62%2A3.54+%2Acos%28+C%29
34.4569+=+21.3444+%2B+12.5316+-32.7096+%2Acos%28+C%29
34.4569+-21.3444+-+12.5316+=-32.7096++%2Acos%28+C%29
0.5809+=-32.7096++%2Acos%28+C%29
32.7096%2Acos%28+C%29=+-0.5809

cos%28+C%29=-0.5809%2F32.7096
cos%28+C%29=-0.0177593122508376745664881258
+C=cos%5E-1%28-0.0177593122508376745664881258%29
+C=91.017587133814283240708188582°
+C=91.0°

B=180-%2890.0%2B51.9%29°
B=38.1°