Question

line makes an angle of 30° with the positive direction of X- axis. So the slope of the line is .......... .Fill in the blank using correct alternatives.
(A)1/2
(B)√3/2
(C)1/√3
(D) √3

Answer 1

we know, if any line makes an angle with positive direction of $\blue{x-axis}$, then tangent of that angle is known as $\red{slope}$. I mean, if A is the angle made by line with positive direction of x- axis then slope of line = tanA

$\bf{Here,}$ line makes an angle of 30° with the positive direction of X - axis.
so, the $\red{slope}$ of given line = tan30° = 1/√3

hence, option (c) is correct.

Answer 2

Hey there !

Solution :

We know that,

Slope = Tan Ф

Slope is also equal to the Opposite side divided by Adjacent side. According to the question,

Ф = 30°

So let the angle be marked at ( 5,0 ) be 30° ( Refer Attachment )

Now we know that,

Ф = 30°

So Slope = Tan Ф,

=> Tan 30° = Tan Ф 

=> Slope = 1 / √ 3

Hence option ( c ) is correct.

Hope my answer helped !