Answer:
a) 5.83 cm
b) 34.45°
Step-by-step explanation:
a) From Pythagoras theorem of right triangles, given right triangle ABC:
AB² + BC² = AC²
Therefore:
AC² = 5² + 3²
AC² = 25 + 9 = 34
AC = √34
AC = 5.83 cm 
b) From triangle ACD, AC = 5.83 cm, AD = 4 cm and ∠A = 90°.  
From Pythagoras theorem of right triangles, given right triangle ACD:
AD² + AC² = DC²
Therefore:
DC² = 5.83² + 4²
DC² = 34 + 16 = 50
DC = √50
DC = 7.07 cm 
Let ∠ACD be x. Therefore using sine rule:

 
        
             
        
        
        
The answer is the third option
        
             
        
        
        
Answer:
The answer to your question is x = 17.32; y = 8.67
Step-by-step explanation:
Process
1.- Use trigonometric functions to find x and y
    a) sin Ф = 
       Ф = 60°
       opposite side = 15
       hypotenuse = ?
      
      
      
             hypotenuse = 17.32
      b) cosФ = 
          
          
                 y = 8.67
 
        
             
        
        
        
Answer:
12:44, or if simplified 3:11
Step-by-step explanation:
In mathematics, a ratio indicates how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8∶6, which is equivalent to the ratio 4∶3). Similarly, the ratio of lemons to oranges is 6∶8 (or 3∶4) and the ratio of oranges to the total amount of fruit is 8∶14 (or 4∶7).
 
        
                    
             
        
        
        
Answer:
7
/10  0.7
Step-by-step explanation:
To add fractions, find the LCD and then combine.