5
If  tan θ  =  —— , calculate the value of  cos θ:
                     4
Recall the definition of the tangent function:
                 sin θ
tan θ  =  ————
                cos θ
 
  5           sin θ
——  =  ————
  4          cos θ
Cross multiply:
5 · cos θ = 4 · sin θ
Square both sides:
(5 · cos θ)² = (4 · sin θ)²
5² · cos² θ = 4² · sin² θ
25 · cos² θ = 16 · sin² θ
But  sin² θ = 1 – cos² θ.  Substitute that for  sin² θ  into the equation above, then you get
25 · cos² θ = 16 · (1 – cos² θ)
25 · cos² θ = 16 – 16 · cos² θ
Isolate  cos² θ:
25 · cos² θ + 16 · cos² θ = 16
(25 + 16) · cos² θ = 16
41 · cos² θ = 16
 
                    16
cos² θ  =  ———
                    41
                      4²
cos² θ  =  ————
                  (√41)²
Take square root of both sides:
 
                       4
cos θ  =  ±  ———
                    √41
                       4                                    4
cos θ  =  –  ———     or     cos θ  =  ———          ✔
                     √41                               √41
The sign of  cos θ  depends on which quadrant  θ  lies. Since you first have a positive value for  tan θ, then that means  θ  lies either in the  1st  or the  3rd quadrant.
•  If  θ  is a  1st  quadrant angle, then
cos θ > 0
 
                   4
cos θ  =  ———          ✔
                 √41
•  If  θ  is a  3rd  quadrant angle, then
cos θ < 0
 
                       4
cos θ  =  –  ———          ✔
                     √41
I hope this helps. =)
        
             
        
        
        
For this case we can model the problem as a rectangle triangle.
 We know:
 Length of the sides of the triangle
 We want to know:
 Length of the hypotenuse
 Using the Pythagorean theorem we have: 

 Rewriting the expression we have: 
 
  
 
 Then, the distance that he would have saved if he travels directly is: 
 Answer:
 Answer:
 he would have saved:
 1.8 miles
 
        
        
        
A. (4+16)/2 = (4+10+16)/3 =10
        
             
        
        
        


 <- Distributive Property

 <- Combine Like Terms
If you're trying to solve for 0:


 <- Subtracted 18 from both sides

 <- Divided both sides by 60 and then simplified.

 <- Fraction Form

 <- Decimal Form
Give Brainliest for simple answer plz :P