Question

Help FAST please!!!!


Right triangle ABC has a right angle C, and the measure of angle A=60 degrees. Given AC=4 units, which of the following is the exact length of segment BC? []= square root sign
4 units
4[3] units
4[2] units
8 units

Answer 1

The correct answer is:  [B]:  " 4√3 units " .
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Explanation:
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Given the following right triangle:  (NOTE:  Not to scale at all!) :

   A
   |   \ 
   |     \
   | 60  \  
   |         \ 
4 |          \ 
   |           \
   |---         \
   |_ |___ _\            
C      x        B
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Solve for "x" .
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"x" = the exact length of segment "BC" .
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Note:  Remember the mnemonic:  "SOH CAH TOA" ; 

in which:  "SOH :  sin = opposite/ hypotenuse;

                 "CAH: cos = adjacent/ hypotenuse; 

                 "TOA":  tan = opposite/adjacent.
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With the information we have at this point, we can use:  "TOA";

that is:  "tangent = opposite/ adjacent" ; to solve for "x" ;

that is:  tan 60 = x / 4 ;  Solve for "x" ; 

↔  x / 4 = tan 60 ; 

Multiply EACH SIDE of the equation by "4" ; 
 to isolate "x" on one side of the equation ; & to solve for "x" ; 

   4 * (x/4) = 4 tan 60 ; 

x = 4 * tan 60 ; 

x = 4* 1.732050807569 ; 

x = 6.928203230276 ;

The answer choices given are: 

Choice  [A}:  4 units;  which is incorrect; since "4 ≠ 6.928203230276" ; 

Choice  [B]:  4√3 units; 

Choice  [C]:  4√2 units; 

Choice  [D]:  8 units; which is incorrect; since "8 ≠ 6.928203230276" .
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We are left with choices [B] and [C].

Let us try both answer choices:

Choice [B]:  "4*√3" = 4 * 1.7320508075688773 = 6.9282032302755092 ;
       → which is the correct answer ;
                  since:  "6.9282032302755092 = 6.9282032302755092" . 
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Choice [C]:  "4*√2" = 4 * 1.414213562373095 = 5.6568542494923802 ;
                            This choice is INCORRECT ;  since:
                        "5.6568542494923802 ≠  6.9282032302755092" .
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The correct answer is:  [B]:  " 4√3 units " .
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Answer 2

if you guys would like to check your answers~

Which of the following is the exact value of cot 60°?

$\frac{1}{\sqrt{3} }$

A 30 ft. ladder is leaning against a building. The ladder reaches the bottom of a window that is located 15 ft. above the ground. What angle does the ladder make with the ground?

30°

Which angle forms a y-coordinate on a unit circle of $\frac{\sqrt{3}}{2}$?

60°

Right triangle ABC has right angle C, and the measure of angle A = 60°. Given AC = 4 units, which of the following is the exact length of segment BC?

$4\sqrt{3}$ units