Question

In the figure ABC is a right angle triangle in which angle B is 90°
BC = 6 cm, angle C is 60° then the length of AC is,
A) 12cm
$b)\frac{12}{ \sqrt{3} } cm$
$c) \: 6 \sqrt{3} cm$ D) 10cm​

Answer 1

Answer:12cm

Step-by-step explanation:

Since here only one side is given, then you have to consider sin,cos,tan

         sin                         cos                    tan

Opposite side       Adjacent side        Opposite side

Hypotenuse           Hypotenuse          Adjacent side

There is only one angle given here apart from the right angle.

Here, we have to find, AC (hypotenuse) and the side BC, which happens to be adjacent to 60 degree is given.

The only trigonometry function which includes both Hypotenuse and Adjacent is cos.

cos 60 =  Adjacent side

                 Hypotenuse

           = 6cm

                 x

Value of cos 60 is 1/2

So, $\frac{1}{2}x = 6$

$x=$6 ÷ $\frac{1}{2}$

  = 6  x 2

  = 12cm

Hope it was understandable.

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Answer 2

Answer:

$A) \: 12 \: cm$$\cos60 \degree = \frac{Base}{Hypotenuse} = \frac{6}{AC} \\ \cos60 \degree = \frac{6}{AC} \\ \because \: \cos60 \degree = \frac{1}{2} \\ \therefore\frac{1}{2} = \frac{6}{AC} \\ AC = 6 \times 2 \\ AC =12 \: cm$