Trigonometric Ratios in Real Scenarios?

📌 CONCEPT: Trigonometric ratios are used to solve problems involving right-angled triangles, especially in real-life scenarios where the angle of depression or elevation is known. In this case, we need to find the horizontal distance of the boat from the foot of the cliff, given the height of the cliff and the angle of depression.

📐 RULE / FORMULA: The tangent function is used to relate the angle of depression, the height of the cliff, and the horizontal distance of the boat. The tangent of 30° is equal to the ratio of the height of the cliff to the horizontal distance of the boat. This is expressed as tan(30°) = height / distance.

💡 WORKED EXAMPLE: Given the height of the cliff (10 meters) and the angle of depression (30°), we can use the tangent function to find the horizontal distance of the boat. We have tan(30°) = 10 / distance. Using the known value of tan(30°) = 1/√3, we can rearrange the equation to find the distance: distance = 10 / (1/√3) = 10√3 meters.

⚠️ COMMON MISTAKE: Students often forget to consider the angle of depression and directly use the sine or cosine functions, which leads to incorrect results.