Find the equation of the straight line which passes through the point (1, 2) and makes such an angle with the positive direction of x – axis whose sine is $$\dfrac{3}{5}$$.

Asked by Aaryan | 1 year ago |  55

##### Solution :-

A line which is passing through (1, 2)

To Find: The equation of a straight line.

By using the formula,

The equation of line is [y – y1 = m(x – x1)]

Here, sin θ = $$\dfrac{ 3}{5}$$

We know, sin θ = $$\dfrac{ 3}{5}$$

So, according to Pythagoras theorem,

(Hypotenuse)2 = (Base)2 + (Perpendicular)2

(5)2 = (Base)2 + (3)2

(Base) = $$\sqrt{(25 – 9)}$$

(Base)2 = $$\sqrt{16}$$

Base = 4

Hence, tan θ = $$\dfrac{ 3}{4}$$

The slope of the line, m = tan θ

=$$\dfrac{ 3}{4}$$

The line passing through (x1,y1) = (1,2)

The required equation of line is y – y1 = m(x – x1)

Now, substitute the values, we get

y – 2 = ($$\dfrac{ 3}{4}$$) (x – 1)

4y – 8 = 3x – 3

3x – 4y + 5 = 0

The equation of line is 3x – 4y + 5 = 0

Answered by Aaryan | 1 year ago

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