Answer:
see explanation
Step-by-step explanation:
Calculate the distance (d) using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (6, 5) and (x₂, y₂ ) = (- 3, 1)
d = 
   = 
   = 
   = 
 ≈ 9.85 ( to 2 dec. places )
 
        
             
        
        
        
Answer:
Length of right-angle  triangle 'a' = 4
b) 
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Step-by-step explanation:
<u><em>Step(i):-</em></u>
Given  b = 3 and hypotenuse c = 5
Given ΔABC  is a right angle triangle
By using pythagoras theorem
         c² = a² + b²
   ⇒ a² = c² - b²
  ⇒  a² = 5²-3² 
           =25 - 9 
       a² = 16
 ⇒   a = √16 = 4
The sides of right angle triangle  a = 4 ,b = 3 and c = 5
<u><em>Step(ii):-</em></u>
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Answer:  see proof below
<u>Step-by-step explanation:</u>
Given: A + B + C = π    →     C = π - (A + B)
                                     → sin C = sin(π - (A + B))       cos C = sin(π - (A + B))
                                     → sin C = sin (A + B)              cos C = - cos(A + B)
Use the following Sum to Product Identity:
sin A + sin B = 2 cos[(A + B)/2] · sin [(A - B)/2]
cos A + cos B = 2 cos[(A + B)/2] · cos [(A - B)/2]
Use the following Double Angle Identity:
sin 2A = 2 sin A · cos A
<u>Proof LHS → RHS</u>
LHS:                        (sin 2A + sin 2B) + sin 2C




![\text{Factor:}\qquad \qquad \qquad 2\sin C\cdot [\cos (A-B)+\cos (A+B)]](https://tex.z-dn.net/?f=%5Ctext%7BFactor%3A%7D%5Cqquad%20%5Cqquad%20%5Cqquad%202%5Csin%20C%5Ccdot%20%5B%5Ccos%20%28A-B%29%2B%5Ccos%20%28A%2BB%29%5D)


LHS = RHS: 4 cos A · cos B · sin C = 4 cos A · cos B · sin C    
 
        
             
        
        
        
Answer:
2400 slabs. If this helps, please give brainliest!