Answer:
55°
Step-by-step explanation:
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°