Designing a Radar System?

📌 CONCEPT: Inverse trigonometric functions are used to find the angles of right-angled triangles, and they play a crucial role in designing a radar system to detect the angle of an object from a distance.

📐 RULE / FORMULA: The inverse tangent function, denoted as tan^(-1) or arctan, is used to find the angle in a right-angled triangle. The formula to find the angle is θ = tan^(-1)(opposite side / adjacent side).

💡 WORKED EXAMPLE: Suppose a radar system detects an object at a distance of 60 km, and the object's height is 20% of its distance. To find the angle at which the object is detected, we can use the inverse tangent function. Let's assume the height of the object is 12 km (20% of 60 km). Then, θ = tan^(-1)(12 / 48) = tan^(-1)(0.25) = 14.036 degrees.

⚠️ COMMON MISTAKE: Students often forget to check the quadrant in which the angle lies after finding it using the inverse tangent function. It is essential to determine the correct quadrant to get the correct angle, especially in real-world applications like radar systems.