shad is 3ft from a lamppost that is 12 ft high. shad is 5 1/2 ft tall. how long is shad's shadow?
2.54 ft
To calculate the length of Shad's shadow, we can use the concept of similar triangles. The triangle formed by Shad, his shadow, and the lamppost is similar to the triangle formed by Shad, his height, and the lamppost.
Let's represent the length of Shad's shadow as 'x'.
Using the concept of similar triangles, we can set up the following equation:
(Height of Shad) / (Length of Shad's shadow) = (Height of the lamppost) / (Distance from Shad to the lamppost)
Plugging in the given values, we get:
5.5ft / x = 12ft / 3ft
Cross-multiplying, we have:
5.5ft * 3ft = 12ft * x
16.5ft = 12ft * x
To solve for 'x', we divide both sides of the equation by 12ft:
x = 16.5ft / 12ft
Simplifying:
x = 1.375ft
Therefore, the length of Shad's shadow is 1.375 feet.
To find the length of Shad's shadow, we can use similar triangles. The height of the lamppost represents one side of the triangle, and the length of the shadow represents the corresponding side that is proportional to Shad's height. Here's how you can calculate it:
1. Determine the length of Shad's shadow using proportions. The height of the lamppost (12 ft) is to the length of its shadow (x) as Shad's height (5.5 ft) is to his shadow's length.
So, we can set up the proportion: 12/ x = 5.5/ Shad's shadow.
2. Cross-multiply to solve for x (the length of Shad's shadow).
12 * Shad's shadow = 5.5 * x.
3. Simplify the equation:
12 * Shad's shadow = 5.5 * x.
12 * 3 = 5.5 * x. (Substituting Shad's shadow as 3 ft)
36 = 5.5 * x.
4. Solve for x (the length of Shad's shadow) by dividing both sides of the equation by 5.5:
x = 36 / 5.5.
x ≈ 6.55 ft.
Therefore, Shad's shadow is approximately 6.55 feet long.
solve the proportion:
12/3 = 5.5/x