Inverse Trigonometry: A Real-World Application?

📌 CONCEPT: Inverse trigonometric functions are used to find the angle given the ratio of the sides of a right-angled triangle, which is essential in real-world applications such as carpentry, architecture, and construction.

📐 RULE / FORMULA: The inverse trigonometric functions that can be used in this scenario are arcsin, arccos, and arctan. However, in this case, we can use the tangent function, i.e., tan(θ) = opposite/adjacent, to find the angle, and then use the arctan function to get the angle in radians.

💡 WORKED EXAMPLE: (1) Let θ be the angle, tan(θ) = 12° / 4.5 = 0.2667. (2) Use a calculator to find the angle in radians: θ = arctan(0.2667) ≈ 0.2746 radians. (3) To find the distance between the level and the point directly below it, we can use the adjacent side, which is the level's distance from the ground, i.e., 4.5 meters.

⚠️ COMMON MISTAKE: Students often get confused between the tangent and cotangent functions, and fail to use the correct inverse trigonometric function to find the angle.