Question

1. Dibuja el triángulo y halla los ángulos y los lados que se desconocen a) b = 70 cm; c = 85 cm ; a = 100 cm b) a = 18 m ; m∡B = 65°; c = 26 m c) c = 6 dm, a = 7,8 dm ; b = 9,5 dm d) b = 98 cm; m∡A = 15°; c = 125 cm

Answer 1

Resolvemos con los Teoremas del seno y el coseno:

a. b = 70 cm; m∡A = 80°; a = 100cm

c =√a²+b² -2ac*cos80°

c = √(100cm)² + (70 cm)² -2*100cm*70 cm*0,174

c =√10000cm²+ 4900cm² - 2436 cm²

c = 111,64 cm

m∡C = arccos b²+c²-a²/2bc

m∡C = arccos (70)² +(111.64)²- (100)²/2*70*111.64

m∡C = 61,89°

m∡B = 180°-61,89°- 80° = 38,11°

b. m∡A = 35°; m∡B = 65°; c = 98cm

m∡C = 180° -65°-35° = 80°

c/senC = a/senA

98/ sen80° =a /sen35°

a = 98* 0,573 /0,985 = 57 cm

b = 98*sen65°/0,985

b = 90,14 cm

c. c = 36 cm; m∡C = 52° ; b = 46 cm

a = √36² +46² -2*36*46*cos 52°

a = √1296 + 2116 - 2039

a = 37 cm