Can you 'cut' the distance with a right-angled triangle?

📌 CONCEPT: To find the distance from the point on the ground to the base of the tower, we can use trigonometric functions to 'cut' the distance using a right-angled triangle.

📐 RULE / FORMULA: The sine rule can be used here, which states that the ratio of the length of a side of a triangle to the sine of its opposite angle is constant for all three sides.

💡 WORKED EXAMPLE: Let's apply the sine rule to find the distance from the point on the ground to the base of the tower. Given: distance from tower to point = 5√3 meters, angle = 60°. We need to find the distance from the point to the base of the tower. Using the sine rule, we have: tan(60°) = opposite side (distance from tower to point) / adjacent side (distance from point to base of tower). Solving for the adjacent side, we get: adjacent side = opposite side / tan(60°) = 5√3 / √3 = 5 meters.

⚠️ COMMON MISTAKE: Students often forget to consider the correct angle and use the wrong trigonometric function, such as using cosine instead of sine.