19. MODELING REAL LIFE A saguaro cactus casts a shadow that is 30 feet long. At the same time, a person standing nearby who is 5 feet 10 inches tall casts a shadow that is 50 inches long. How tall is the cactus? Example 3

To find the height of the saguaro cactus, we can use the concept of similar triangles caused by the sun's rays. Since the cactus and the person are both casting shadows, we can set up a ratio. The height of the cactus (let’s call it \( h \)) over its shadow length (30 feet) equals the height of the person (5 feet 10 inches, which is 70 inches) over the shadow length of the person (50 inches). So, the equation is \( \frac{h}{30} = \frac{70}{50} \). Solving this will give us the height of the cactus! Once you set up that ratio, remember to convert everything into the same units to make calculations easier. You could either convert the cactus's shadow into inches or the person’s height into feet; just be consistent! After solving for \( h \), you may discover that the cactus measures a towering height, standing proudly under the sun, just like its human neighbor. Happy calculating!