Jonathan is 3 ft from a lamppost that is 12 ft high. The lamppost and it's shadow form the legs of a right triangle. Jonathan is 6 ft tall and Is standing parallel to the lamppost. How long is Jonathan's shadow?
I don't get how the answer is square root 180, Ryan?
How are you supposed to know which direction the shadow is facing? Or what side of the lamppost he is standing on?
Actually, it's sqrt(180) from the top of the pole to the tip of the shadow.
Using similar triangles, if the shadow is x feet long,
12/(3+x) = 6/x
12x = 18 + 6x
6x = 18
x = 3
so, the shadow is 3 feet long.
To find the length of Jonathan's shadow, we can use the concept of similarity of triangles. Since the lamppost and its shadow form the legs of a right triangle, and Jonathan is standing parallel to the lamppost, we can consider the lamppost and Jonathan as two similar triangles.
The height of the lamppost is 12 ft, and Jonathan's height is 6 ft. Therefore, the ratio of their heights is 12/6 = 2.
Now, let's consider their respective distances from the lamppost. Jonathan is 3 ft away from the lamppost, while the shadow is the corresponding distance away from the lamppost. So, the ratio of their distances from the lamppost is also 2.
Since the triangles are similar, the ratio of their corresponding sides is equal. Therefore, the length of Jonathan's shadow would be 3 ft * 2 = 6 ft.
Hence, the length of Jonathan's shadow is 6 ft, not the square root of 180.
To find the length of Jonathan's shadow, you can use the concept of similar triangles. Similar triangles have corresponding sides in proportion to each other.
In this scenario, we can consider two similar triangles: the triangle formed by the lamppost, its shadow, and the ground, and the triangle formed by Jonathan, his shadow, and the ground.
Let's label the lengths of the sides:
- Length of Jonathan: J = 6 ft
- Distance of Jonathan from the lamppost: AJ = 3 ft
- Height of the lamppost: LH = 12 ft
- Length of the lamppost shadow: LK = ?
Based on the concept of similar triangles, the ratio of corresponding sides will be equal in both triangles. So, we have the following proportion:
(Jonathan's height) / (Jonathan's shadow) = (Lamppost height) / (Lamppost shadow)
Plugging in the given values, we get:
6 ft / LK = 12 ft / 3 ft
Simplifying the proportion, we have:
6 / LK = 12 / 3
Cross-multiplying, we get:
6 * 3 = 12 * LK
18 = 12LK
Dividing both sides by 12, we find:
LK = 18 / 12
LK = 1.5 ft
So, Jonathan's shadow is 1.5 ft long, not √180 ft.
It seems there might be an error or misunderstanding in Ryan's explanation. The correct answer is 1.5 ft.