solucione los siguientes triangulos: a) b= 20cm, c= 28cm, angulo c= 40° b) a= 4 1cm, b= 9cm, c= 40cm por favor es para hoy, espero que me ayuden. : )
Respuestas
Respuesta:
a) a = 46.2 cm
∡A = 112.68°
∡B = 27.32°
b) ∡A = 90°
∡B = 12.68°
∡C = 77.32°
Explicación paso a paso:
a) Debemos aplicar la ley de los senos
a/sen A = b/sen B = c /sen C
Calculamos primero "∡B"
b/sen B = c/sen C
20/sen B = 28/sen 40°
sen B = 20 sen 40° / 28
sen B = 20 ( 0.6427 ) / 28
sen B = 0.459
∡B = sen⁻¹ 0.459
∡B = 27.32°
Calculamos "∡ A"
∡A = 180 - ( 40 + 27.32 )
∡A = 180 - 67.32
∡A = 112.68°
calculamos "a"
a/sen A = b/sen B
a/sen 112.68 = 20/sen 27.32
a = 20 sen 112.68 / sen 27.32
a = 20 ( 0.9226 ) / 0.4589
a = 18.452/0.4589
a = 46.2 cm
b) utilizaremos la ley de los cosenos
Calculamos "∡A"
a² = b² + c² - 2bc cos A
cos A = a² - ( b² + c² ) / - 2bc
cos A = ( 41 )² - [ ( 9 )² + ( 40 )² ] / - 2 ( 9 ) ( 40 )
cos A = 1681 - ( 81 + 1600 ) / - 720
cos A = 1681 - 1681 / - 720
cos A = 0/ -720
cos A = 0
∡A = cos⁻¹ 0
∡A = 90°
Calculamos "∡B"
b² = a² + c² - 2ac cos B
cos B = b² - ( a² + b² ) / - 2ac
cos B = ( 9 )² - [ ( 41 )² + ( 40 )² / - 2 (41 ) ( 40 )
cos B = 81 - ( 1681 + 1600 ) / - 3280
cos B = 81 - 3281 / - 3280
cos B = - 3200 / - 3280
cos B = 0.9756
∡B = cos⁻¹ 0.9756
∡B = 12.68°
Calculamos "∡C"
∡C = 90 - 12.68 ( recordemos que ∡A = 90° )
∡C = 77.32°