The slopes of two lines are 1 and
3
. What is the angle between these two lines?
- A15
∘ - B30
∘ - C45
∘ - D60
∘
Solution & Step-by-step Explanation
Let the slopes of the two lines be m
1
=1 and m
2
=
3
.
The acute angle θ between two lines is given by the formula:
tanθ=
1+m
1
m
2
m
2
−m
1
Substituting the given values:
tanθ=
1+1×
3
3
−1
=
3
+1
3
−1
To simplify, multiply the numerator and denominator by (
3
−1):
tanθ=
(
3
)
2
−1
2
(
3
−1)
2
=
3−1
3+1−2
3
=
2
4−2
3
=2−
3
We know that:
tan(15
∘
)=2−
3
Therefore, θ=15
∘
.
1
=1 and m
2
=
3
.
The acute angle θ between two lines is given by the formula:
tanθ=
1+m
1
m
2
m
2
−m
1
Substituting the given values:
tanθ=
1+1×
3
3
−1
=
3
+1
3
−1
To simplify, multiply the numerator and denominator by (
3
−1):
tanθ=
(
3
)
2
−1
2
(
3
−1)
2
=
3−1
3+1−2
3
=
2
4−2
3
=2−
3
We know that:
tan(15
∘
)=2−
3
Therefore, θ=15
∘
.