Question

The distance between the points \( (5\cos 0, 0) \) and \( (0, 5\sin 0) \) is:

• A. \( 10 \)
• B. \( 5 \)
• C. \( 30 \)
• D. \( 25 \)

Hint:

The distance between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}. \]

Answer 1

The Correct Option is B

The given points are:
\[ A(5\cos 0, 0) = (5,0) \quad \text{and} \quad B(0, 5\sin 0) = (0,5). \] Using the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] \[ = \sqrt{(0 - 5)^2 + (5 - 0)^2} \] \[ = \sqrt{(-5)^2 + (5)^2} \] \[ = \sqrt{25 + 25} = \sqrt{50} \approx 5. \]