A lamppost casts a shadow that is 24 feet long. Tad, who is 6 feet tall, is standing directly next to the lamppost. his shadow is 15 feet long. How tall is the lamppost?
Use a proportion. Cross multiply and solve for x.
6/15 = x/24
To find the height of the lamppost, we can use proportions.
Let's assume H represents the height of the lamppost.
According to the given information, the height of Tad is 6 feet, and his shadow is 15 feet.
The lamppost's shadow is 24 feet.
We can create a proportion using these values:
Height of Tad / Length of Tad's shadow = Height of lamppost / Length of lamppost's shadow
Plugging in the given values, we get:
6 feet / 15 feet = H / 24 feet
Cross multiply:
6 feet * 24 feet = 15 feet * H
144 feet = 15 feet * H
Divide both sides of the equation by 15 feet to solve for H:
H = 144 feet / 15 feet
Simplifying the division, we get:
H = 9.6 feet
Therefore, the height of the lamppost is 9.6 feet.
To find the height of the lamppost, we can set up a proportion using the ratios of the corresponding sides of the triangles formed by the lamppost, Tad, and their shadows.
Let's call the height of the lamppost "h".
In the first triangle, the height of the lamppost corresponds to the length of its shadow, so we have the ratio:
h / 24 = 6 / 15
To find the height of the lamppost, we can cross-multiply and solve for h:
15h = 6 * 24
15h = 144
h = 144 / 15
Therefore, the height of the lamppost is 9.6 feet.