Mathematics
The given figure represents the lines y = x + 1 and y = Write down the angles which the lines make with the positive direction of the x-axis. Hence, determine θ.
Straight Line Eq
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Answer
Given,
y = x + 1 and y = .
Comparing equations with y = mx + c we get,
m1 = 1 and m2 = .
Let the first line make angle θ1 and second make θ2 with positive direction of x-axis.
The inclination that y = x + 1 makes is,
⇒ m1 = tan θ1 = 1
⇒ tan θ1 = 1 = tan 45°
⇒ tan θ1 = tan 45°
⇒ θ1 = 45°.
The inclination that y = - 1 makes is,
⇒ m2 = tan θ2 =
⇒ tan θ2 = = tan 60°
⇒ tan θ2 = tan 60°
⇒ θ2 = 60°.
From graph we get,
60° is the exterior angle. We know that,
Exterior angle = Sum of two opposite interior angles.
∴ 60° = θ + 45°
⇒ θ = 60° - 45°
⇒ θ = 15°
Hence, y = x + 1 makes 45° and y = makes 60° with the x-axis. The value of θ = 15°.
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