Question

Solve A ABC subject to the given conditions, if possible. Round the lengths of sides and measures of the angles (in degrees) to 1 decimal place if necessary. Round intermediate steps to four decimal places. a=16, b=19, c=18 The triangle with these conditions does not exist. х 5 O The triangle with these conditions does exist. O A A= B~ O Ca

Answer 1

Solution an given that, a triangle which sicks a= 16, b = 19, C = 18 с 6=19 q=16 А B C-18 to find the angle we will use cosine Rule, Cosine Rule is- COSA = 62 +c2-92 a abc B A с LOSB = a²+c²- 6² 2ac Cosc a²+6²_c² = 2ab so here For angle A COSA = 6² +c²- a2 abc (19)2+(18)2-(16)2 COSA = 2X19X18 361 + 324 - 256 684 COSA 685-256 684

Cosa 429 684 COSA 0.6271 A = cost (0.6271.) A = 51,10 For angle B, a²+c²_62 CO SB = 2ac LOSB (16)2 + (18)2-(1992 2 X16X18 COSB 256 + 324 - 361 576 COSB 5B0-361 576 219 COSB 576 CosB = 0.380 2 se cost (0.3802) B = 67.5°

For angle c, Cosc a2 +6²_ca 2a6 COSC 16²+ 192 182 2 X16X19 los c = 256+ 361 - 324 608 cosc 617 - 324 608 Cosc = 293 608 cosc = 0.4819 CE cost(0.4819) c = 61.10