Shalonda notices that when she stands next to the flagpole, she casts a shadow that is 8 feet long and that the flagpole casts a shadow that is 28 feet long. Little Shalonda is 4 feet tall. How tall, to the nearest foot, is the flagpole?
step by step on how to do it?
the pole is 69 feet
also 420 ft will work
Seet up a proportion of Shadow/height for each object. So Shalonda would be 8/4 and the flagpole would be 28/x. so 8/4 = 28/x. Cross multiply and divide. (28 X 4) / (8x) or 112/8 = x. So the pole is 14 feet tall which makes sense if her shadow is twice as long as she is tall, so is the flagpole's.
To find the height of the flagpole, we can use similar triangles. Here are the steps:
Step 1: Identify the similar triangles:
In this scenario, we have two right-angled triangles - one formed by Shalonda and her shadow, and the other by the flagpole and its shadow. These two triangles are similar because they have the same shape, but different sizes.
Step 2: Determine the corresponding sides:
In the first triangle, we have the height of Shalonda, which is 4 feet, and the length of her shadow, which is 8 feet.
In the second triangle, we need to find the height of the flagpole and the length of its shadow, which is given as 28 feet.
Step 3: Set up the proportion:
Since the triangles are similar, the ratios of their corresponding sides will be equal. We can set up the proportion using the heights and the lengths of the shadows:
(height of Shalonda) / (length of Shalonda's shadow) = (height of the flagpole) / (length of the flagpole's shadow)
Plugging in the values: 4/8 = (height of the flagpole) / 28
Step 4: Solve for the height of the flagpole:
Cross-multiplying the proportion, we get (4 * 28) = 8 * (height of the flagpole)
112 = 8 * (height of the flagpole)
Now, we can solve for the height of the flagpole by dividing both sides of the equation by 8:
height of the flagpole = 112 / 8 = 14
Therefore, the height of the flagpole is 14 feet (to the nearest foot).