Matematicas 1 (Arquitectura)

Secantes

   2x

                       3x – 20                     

Y + 10

2x = 3x -20                               3(20) – 20 =                         y + 10 = 40
20 = 3x -2x                               60 – 20 = 40                        y = 40 -10
20 =x                                                                                       y = 30

     X + 2y
          4y

92°

X + 2y = 92             92 + 4y = 180
x + 2(22) = 92            4y = 180 - 92     
x + 44 = 92                                          4y = 88
x = 92 – 44                                          y =
x = 48                                                   y = 22

 

8x + 5y        9x - 2y

70°                   57°

8x + 5y = 70                                9(5) + 2y = 27
9x – 2y = 57                                45 + 2y = 57
16 – 10y = -140                          2y  = 57 - 45
45 + 10y = 289                           2y  = 12    
9x          = 145                             y =
x =                            y = 6
X = 5

Teoremas

.- Si uno de los ángulos agudos de un triangulo rectángulo es el doble del otro, cuanto miden esos Angulo?

2y

90°                 x                   2x + x = 90
                                              3x = 90
                                              x =        
                                              x = 30      

.-Si uno de los ángulos agudos de un triangulo rectángulo es un tercio de otro cuanto miden eses ángulos?

x

90°                   x                  x + x = 90              4x = (90) (3)        
                                              x +  = 90               4x = 270         = 22.5
                                              x = 90                     x =    
                                                                                  x = 67.5 

.-Si el ángulo “B” excede en 18° al ángulo “A” y el ángulo “C” es la mitad del ángulo “B”, cual es el valor de cada ángulo?

             B                          A = 61.2                              A + A + 18 +  = 180

   A                 C                B =  79.2                              2A + 18 +  +  = 180

                                         C =  39.6                              2A +  + 9 = 180 - 18

                                                                                      2A +  = 180 – 18 - 9

                                                                                2A +  = 153
                                                                                +  =
                                                                               = 153
                                                                                = 153
                                                                               5A = (153) (2)
                                                                               5A = 306
                                                                               A =    
                                                                               A = 61.2   

                                                                               

                                          A = 50                                       50°    y =                             X = 50
                       x=               X = 50                                                                                    Y = 95
                                          Y = 130                       

80°                         
                                    y =                                           X =                    45°

Teorema de Pitágoras

A = 3                              B = 4                              C = 5
 (3)²                                (4)²           9 + 16
 9             16             25 =  = 5

A = 15                              B = 8                              C = 17
(15)²                              225 - 289                (17)² 
225                                 64 =  = 8           289

Hipotenusa
.-Calcular la altura de un triangulo equilátero que mide 10 metros por lado
                                     

                    C =                 A = 25
              B =                       B = 8 .6
                                          C = 100

   10        A=  5       

.-Cuanto mide la diagonal de un cuadrado de 5 metros por lado

                                          B = (5)² = 25       A = 25                       25 + 25 = 50
                      C =                                                   B = 25                          = 7 .07
                                                                              C = 7 .07
                 A = 5
                  (5)² = 25
                  

Polígonos
.-Calcular el área de un hexágono, si su apotema es 8.66 y cada uno de sus lados 12

                     12           12  6 = 72  2 = 36  8.66 = 311. 76 cm²

             8.66 

.-Calcular el perímetro de un hexágono, si su área es de 1200 m² y su apotema de
          1200m²                       . 8 = 1200                  p = (150) (2)          =   
                   =       p = 300       = 50
       8           = 150     

Ángulos adyacentes 
                                                             65 32 28
  x =65° 32’’ 28’                                 89 59 60
                                                           24° 27’ 32’’

            y = 24° 27’’ 32’

                                                                   123 32 26
y = 123° 32’’ 26                                       179 59 60
                                                                    56° 27’’ 34’
                                   x = 56° 27’’ 34’

 Grados y Radianes

223° = (223) (0.017453) = 3.89 rad.
58° 39’’ 48’ = 1.02 rad  
 = .8      
 39 + .8 = 39.8    
 =  .66
58 + .66 = 58.66
58.66 (0.017453) = 1.02