Resuelve los siguientes triángulos rectángulos encontrando todos los datos faltantes
1 answer:
Respuesta:
A = 51,167
b = 28,5 pies
c = 45,4 pies
Explicación paso a paso:
C = 90 °
B = 38 ° 50 '
Convertir B a grado
1 ° = 60 '
x ° = 50 '
Multiplicar en cruz:
60x = 50
x = 50/60
x = 0,83333 °
Por lo tanto, 38 ° 50 '= 38 ° + 0.833 ° = 38.833 °
Recordar :
A + B + C = 180 ° (Suma de ángulos en un triángulo)
A + 38.833 + 90 = 180
A + 128.833 = 180
A = 180 - 128,833
A = 51,167 °
Usando identidades trigonométricas, podríamos encontrar byc
Para obtener b:
Tan B = opuesto / adyacente = b / 35.4
Tan 38,833 = b / 35,4
b = Tan 38,833 * 35,4
b = 28,5 pies
Para obtener c:
Podríamos usar:
Sin A = opuesto / hipoteno = 35,4 / c
Sin 51,167 = 35,4 / c
c * sin 51,167 = 35,4
c = 35,4 / sen 51,167
c = 45,4 pies
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We can replace secθ with 1/cosθ in our expression.
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We can replace sinθ/cosθ with tanθ.
Now we have as our final answer:
Hope this helps!