A post stands vertically in horizontal ground such that 80 cm of the post is above ground Find the length of its shadow when the elevation of the sun is \( 40^{\circ} \).

To find the length of the shadow cast by the post, we can use trigonometry. When the sun is at an elevation of \( 40^{\circ} \), the height of the post above the ground (80 cm) acts as the opposite side of a right triangle, and the length of the shadow will be the adjacent side. Using the tangent function: \[ \tan(40^{\circ}) = \frac{\text{height of the post}}{\text{length of the shadow}} \] Let the length of the shadow be \( x \). Then: \[ \tan(40^{\circ}) = \frac{80}{x} \] Rearranging gives us: \[ x = \frac{80}{\tan(40^{\circ})} \] Using a calculator, \(\tan(40^{\circ}) \approx 0.8391\): \[ x \approx \frac{80}{0.8391} \approx 95.2 \text{ cm} \] So, the length of the shadow is approximately \( 95.2 \) cm. To get the best visual experience, remember this is like a fun game of angles and heights! You simply use the magic of triangles to find out how long the shadow is based on the sun's position. And voilà, you've just applied some geometry to real-life scenarios—like figuring out when to put on sunscreen or when it's time to play in the shade!