Solve triangle ABC. (If an answer does not exist, enter DNE. Round your answers to one decimal place.) a = 25, b = 34, c = 26

Answer 1

sides 25, 26 and 34 find the semi perimeter (25+26+34)/2 = 85/2 = 42.5

find the area using Heron's formula

A = sqr(42.5)(42.5-34)(42.5-26)(42.5-25))

=sqr((42.5)(8.5)(16.5)(17.5))

= about 323

a=25, c=26, b=34

use the law of cosines to find an angle

c^2 = a^2 + b^2 - 2abCosC

26^2 = 25^2 +34^2 - 2(25)(34)CosC

CosC = (676 - 625- 1156)/-1700

= .65

C = about 49.5 degrees

use the law of cosines to find the other 2 angles, or use the law of sines

sinB/b = sinC/c

sinB/34 = sin49.5/26

B = 83.9

C =49.5

A = 180-83.9-49.5

= 46.6 degrees for Angle A

it's almost a right triangle, so the area should be close to (25(26)/2 = 325