Question

Find the angle, correct to two decimal places, that the lines joining the given points make with the positive direction of the x-axis:(3b,a), (3a,b)

Answer 1

The angle the line joining the given points make with the positive direction of the x-axis is 341.56°

The angle Ф between two points (x₁,y₁) and (x₂,y₂) is gotten from tanФ = (y₂ - y₁)/(x₂ - x₁).

Since (x₁, y₁) = (3b, a) and (x₂, y₂) = (3a, b)

Substituting the values of the variables into the equation, we have

tanФ = (y₂ - y₁)/(x₂ - x₁)

tanФ = (b - a)/(3a - 3b)

tanФ = -(a - b)/3(a - b)

tanФ = -1/3

taking inverse tan of both sides, we have

Φ = tan⁻¹(-1/3)

Φ = -tan⁻¹(1/3)

Φ = -18.43°

Converting to a positive angle, we have

Φ = -18.43° + 360°

Φ = 341.56°

So, the angle the line joining the given points make with the positive direction of the x-axis is 341.56°

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