Dibuja el triángulo y halla la medida de los ángulos y los lados que faltan.
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. mxC = 41%; b= 105 m; a = 140 m
e. b = 98 cm; mA = 15%; c= 125 cm
Respuestas
Respuesta:
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
BY: @Luismgalli
Explicación paso a paso:
Respuesta: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
BY: @Luismgalli
Explicación paso a paso:
Explicación paso a paso: