Final answer:
The correct equation of the line is (d) x + √3 y = 10, which is derived using trigonometric relations and the general equation of a line based on the given perpendicular length and angle with the x-axis.
Step-by-step explanation:
The student is asking for the equation of a line where the length of the perpendicular from the origin is 5 and the angle of this perpendicular with the x-axis is 60°. To solve this, we will use trigonometric relations and the general equation of a straight line. First, we need to identify the x and y intercepts based on the given angle and the length of the perpendicular.
Using the formula Ax = A cos θ and Ay = A sin θ, where A is the length of the perpendicular, we calculate the intercepts. For a perpendicular length (A) of 5 and an angle (θ) of 60°, the x-intercept (Ax) is 5 cos 60° = 2.5 and the y-intercept (Ay) is 5 sin 60° = 4.3301 (approximately √3 * 2.5).
The equation of the line can be given by x/Ax + y/Ay = 1, substituting the found x and y intercepts, we have x/2.5 + y/(4.3301) = 1, which simplifies to x + √3 y = 10. Therefore, the correct equation of the line is equation (d).