Question

Find the obtuse angle between the following pair of straight lines.


`y = - 2 \: and \: y = √(3)x - 1`
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Answer 1

Given:

`y=-2`

`y=√(3)x-1`

To find:

The obtuse angle between the given pair of straight lines.

Solution:

The slope intercept form of a line is

`y=mx+b` ...(i)

where, m is slope and b is y-intercept.

The given equations are

`y=0x-2`

`y=√(3)x-1`

On comparing these equations with (i), we get

`m_1=0`

`m_2=√(3)`

Angle between two lines whose slopes are
`m_1\text{ and }m_2` is

`\tan \theta=\left|(m_2-m_1)/(1+m_1m_2)\right|`

Putting
`m_1=0` and
`m_2=√(3)`, we get

`\tan \theta=\left|(√(3)-0)/(1+(0)(√(3)))\right|`

`\tan \theta=\left|(√(3))/(1+0)\right|`

`\tan \theta=\pm √(3)`

Now,

`\tan \theta= √(3)` and
`\tan \theta=-√(3)`

`\tan \theta= \tan 60^\circ` and
`\tan \theta=\tan (180^\circ-60^\circ)`

`\theta= 60^\circ` and
`\theta=120^\circ`

`120>90`, so it is an obtuse angle and
`60<90`, so it is an acute angle.

Therefore, the obtuse angle between the given pair of straight lines is 120°.