Question

Find the slip of a line whose inclanation is 15°

Answer 1

Solution :-

Slope is the numeric description of the steepness of a line. Slope of a line is given by the tangent of inclination and is denoted by m i.e. tan θ = m.

In the question, we are asked to find the slope of a line whose inclination is 15°.

So, the slope of the line is given by,

⇒ Slope, m = tan θ

⇒ Slope, m = tan 15°

⇒ Slope, m = tan ( 45° - 30° )

As we know that,

• tan ( A - B ) = (tan A - tan B) / (1 + tan A. tan B)

⇒ Slope, m =( tan 45° - tan 30° )/( 1 + tan 45° . tan 30° )

⇒ Slope, m = ( 1 - 1/√3 ) / ( 1 + (1)(1/√3) )

⇒ Slope, m = (√3 - 1 )/√3 ÷ (√3 + 1)/√3

⇒ Slope, m = ( √3 - 1 ) / (√3 + 1 )

On rationalising,

⇒ Slope, m = (√3 - 1) / ( √3 + 1 ) × (√3 - 1 ) / (√3 - 1 )

⇒ Slope, m = (√3-1 )² / ((√3)² - 1)

⇒ Slope, m = ((√3 ) ² + 1 - 2√3) / 2

⇒ Slope, m = (3 + 1 - 2 √3) / 2

⇒ Slope, m = 4 - 2√3 / 2

⇒ Slope, m = 2 - √3

⇒ Slope, m = 2 - 1.732

⇒ Slope, m = 0.268

Hence the slope of line which has an inclination of 15° has a slope of 0.268.