A 3ft tall child is standing 9 feet from a lamp post. The lamp post is casting the childs shadow which is 8ft long. Find the height of the lamp post and draw a diagram and illustrate the situation. Explain why the triangles are similar

h/(9+8) = 3/8

Did you know?

Did you know that in similar triangles, corresponding sides are proportional? In this scenario, a 3ft tall child is standing 9ft away from a lamp post. The lamp post is casting a shadow that is 8ft long. By drawing a diagram, we can see that the height of the lamp post is the missing measurement to find. To determine this, we can set up a proportion using the lengths of the child and its shadow, and the unknown height of the lamp post and its corresponding shadow. The proportion can be written as 3ft (child height) / 8ft (child shadow) = x (lamp post height) / 9ft (lamp post shadow), where x represents the height of the lamp post. By cross-multiplying and solving for x, we can calculate the height of the lamp post. Thus, the triangles in this scenario are similar because their corresponding sides, the child's height and shadow, are proportional to the lamp post's height and shadow.