Find the angle between the lines whose
gradients are 4 and 2
A. 12.5°
B.14.1°
C.
26.8°
D. 33.7°
tan75.96° = 4
tan63.43° = 2
so the difference is 12.5°
Pick A.
Note that the question asks for the angle between the two lines, which is not the same as the difference between the angles whose tangents are given. So, your solution is incorrect.
To find the angle between two lines with gradients m1 and m2, we use the formula:
θ = tan⁻¹(|(m1-m2)/(1+m1m2)|)
Substituting m1 = 4 and m2 = 2, we get:
θ = tan⁻¹(|(4-2)/(1+(4)(2))|)
θ = tan⁻¹(2/9)
θ ≈ 12.5°
Therefore, the correct answer is A. 12.5°.
To find the angle between two lines given their gradients, we can use the formula:
angle = tan^(-1) |(m1 - m2) / (1 + m1 * m2)|
where m1 and m2 are the gradients of the lines.
In this case, the gradients are m1 = 4 and m2 = 2. Plugging these values into the formula, we get:
angle = tan^(-1) |(4 - 2) / (1 + 4 * 2)|
angle = tan^(-1) |2 / 9|
Now, use a calculator to evaluate tan^(-1) |2 / 9|, which is approximately 12.5°.
Therefore, the angle between the lines with gradients 4 and 2 is approximately 12.5°.
So, the correct answer is A. 12.5°.
The angle between two lines with gradients m1 and m2 is given by
θ = tan⁻¹(|(m1-m2)/(1+m1m2)|)
In this case, m1 = 4 and m2 = 2, so
θ = tan⁻¹(|(4-2)/(1+(4)(2))|)
θ = tan⁻¹(2/9)
θ ≈ 14.1°
Therefore, the answer is B. 14.1°.