Detailed Summary
In this example, an electrician must repair an electrical fault on a pole height of 5 m. The task requires her to reach a point 1.3 m below the pole's top, making the required vertical reach 3.7 m (5 m - 1.3 m). To successfully calculate the necessary length of the ladder, the problem uses right-angled triangle properties and trigonometric ratios, specifically the sine function. The length of the ladder corresponds to the hypotenuse of the triangle formed.
The sine of the angle (60°) allows us to set up the equation using the formula:
$$\frac{BD}{BC} = \sin(60°)$$
Where BD (the vertical reach) equals 3.7 m, leading to the length of the ladder, BC, being approximately 4.28 m. Additionally, to find how far from the pole the ladder's base should be placed, the cotangent function provides the necessary calculation, yielding a distance of approximately 2.14 m. This example is significant for understanding practical applications of trigonometry in real-world scenarios.