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

if you guys would like to check your answers~

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

`(1)/(√(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
`(√(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√(3)` units

Answer 2

The correct answer is: [B]: " 4√3 units " .
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Step-by-step 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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