A tower casts a shadow of 64 feet. A 6-foot tall pole near the tower casta a shadow 8 feet long. How tall is the tower.
The height-to-shadow-length ratio is the same for both pole and tower. That is because the sun is at the same angle in the sky for both. You have similar right triangles formed by object, its shadow on the ground and the slated sunbeam that comes down to the ground from the top.
Let H be the tower height.
H/64 = 6/8 = 3/4
H = 64*3/4 = 48 feet
The height to the shadow length ratio is the same for both pole and tower. For example H/64=6/8=3/4
H=64*3/4=48feet
To find the height of the tower, we can use ratios and proportions.
Let's set up the proportion:
Height of the tower / Length of the tower's shadow = Height of the pole / Length of the pole's shadow
Let's plug in the values we know:
Height of the tower / 64 feet = 6 feet / 8 feet
Now, we can cross-multiply and solve for the height of the tower:
Height of the tower = (6 feet * 64 feet) / 8 feet
Height of the tower = 384 feet / 8 feet
Height of the tower = 48 feet
Therefore, the height of the tower is 48 feet.
To find the height of the tower, we can use the concept of similar triangles.
First, let's assign variables to the given measurements:
Let h be the height of the tower, and s be the length of its shadow.
Let p be the height of the pole, and x be the length of its shadow.
We have two similar triangles in this scenario:
1. The triangle formed by the tower, its shadow, and the pole.
2. The triangle formed by the pole, its shadow, and the ground.
Using the given measurements, we know that the pole is 6 feet tall and casts a shadow of 8 feet. Therefore, we have:
p = 6 and x = 8.
Now, let's set up a proportion between the corresponding sides of the two similar triangles:
(pole height)/(pole shadow) = (tower height)/(tower shadow)
This can be written as:
p / x = h / s
Substituting the known values, we get:
6 / 8 = h / 64
Next, let's solve for h:
Multiply both sides of the equation by 64:
(6 / 8) * 64 = h
Simplifying the expression:
h = (6 * 64) / 8
h = 48
Therefore, the height of the tower is 48 feet.