Find the angle made by the x axis and the terminal side resulting from connecting the origin to (5,7), rounded to the nearest integer

55°

To solve this, follow these steps:

i. Make a sketch of the problem.

The sketch has been attached to this response.

ii. Label the sketch properly

As shown in the sketch, θ is the angle between the x-axis and the terminal side resulting from connecting the origin to (5,7).

iii. Solve using the tangent trigonometric ratio

With the proper sketch and labelling, a right triangle is formed with the adjacent and opposite sides to the angle being  5 units and 7 units respectively.

Using the tangent formula,

tan θ = opposite / adjacent

tan θ = 7 / 5

θ = tan⁻¹ (7/5)

θ = tan⁻¹ (1.4)

θ = 54.46

θ = 55° to the nearest integer.

Therefore, the angle  made by the x axis and the terminal side resulting from connecting the origin to (5,7), rounded to the nearest integer is 55°

2