Charlene made the sketch below in order to find the height x of a pole. She positioned a mirror on the ground so that she could see the reflection of the top of the pole. Her height, her distance from the mirror, and her line of sight to the mirror determine the smaller triangle. The pole’s height, its distance from the mirror, and the distance from the top of the pole to the mirror form a larger similar triangle. Find the height of the pole to the nearest tenth.
My clairvoyance cap does not seem to be working this afternoon, and I can't see your sketch.
You will just have to provide us with some values in that sketch.
yes
To find the height of the pole, we can use the concept of similar triangles.
In the sketch, we have a smaller triangle formed by Charlene's height, her distance from the mirror, and her line of sight to the mirror. Let's call the height of the smaller triangle "h".
We also have a larger similar triangle formed by the pole's height, its distance from the mirror, and the distance from the top of the pole to the mirror. Let's call the height of the pole "x".
Since the two triangles are similar, we can set up the following proportion:
h / Charlene's distance from the mirror = x / (the pole's distance from the mirror + the distance from the top of the pole to the mirror)
Now, we need to determine the values for h, Charlene's distance from the mirror, the pole's distance from the mirror, and the distance from the top of the pole to the mirror.
Let's assume that Charlene's height is 5 feet and her distance from the mirror is 10 feet. Also, let's say the pole is 20 feet away from the mirror, and the distance from the top of the pole to the mirror is 15 feet.
Now we can substitute these values into the proportion:
h / 10 = x / (20 + 15)
Simplifying, we get:
h / 10 = x / 35
Cross-multiplying, we get:
h * 35 = 10 * x
Simplifying further, we have:
35h = 10x
Dividing both sides by 35, we get:
h = (10/35) * x
Now, we can solve for x by substituting the known value of h. Using a calculator, we find:
x = (35 * h) / 10
Since we know the height of the smaller triangle "h" is 5 feet, we can substitute that value into the equation:
x = (35 * 5) / 10
x = 17.5
Therefore, the height of the pole is approximately 17.5 feet to the nearest tenth.