A 3-ft vertical post casts a 24-in shadow at the same time a pine tree casts a 30-ft shadow. How tall is the pine tree?

Cross multiply and solve for x.

3/2 = x/30

A 4​-ft vertical post casts a 20​-in shadow at the same time a nearby cell phone tower casts a 115​-ft shadow. How tall is the cell phone​ tower?

To solve this problem, we can set up a proportion using the given information.

Let's start by converting the measurements to the same unit. Since the height of the post is given in feet and the shadow of the post is given in inches, let's convert the shadow length to feet:

1 foot = 12 inches

Therefore, the shadow of the post is:
24 inches / 12 inches/foot= 2 feet

Now, we can set up a proportion using the height and shadow length of the post, and the height and shadow length of the pine tree:

Post height / Post shadow length = Pine tree height / Pine tree shadow length

3 feet / 2 feet = Pine tree height / 30 feet

To find the height of the pine tree, we can solve for "Pine tree height" by cross-multiplying:

(Pine tree height) * 2 feet = 3 feet * 30 feet

(Pine tree height) * 2 = 90

Pine tree height = 90 / 2

Pine tree height = 45 feet

Therefore, the pine tree is 45 feet tall.

To determine the height of the pine tree, we can set up a proportion using the lengths of the shadows and the heights of the objects.

Let x be the height of the pine tree in feet.

Using the given information, we can set up the following proportion:

(Height of post)/(Length of post shadow) = (Height of pine tree)/(Length of pine tree shadow)

Substituting the values we have:

3 ft / 24 in = x ft / 30 ft

However, the units need to be consistent, so we need to convert inches to feet.

There are 12 inches in 1 foot, so:

(3 ft) / (24 in) = x ft / (30 ft * 12 in/ft)

Reducing the fraction:

1/8 = x / (30 * 12)

Next, we can cross-multiply and solve for x:

8x = 1 * (30 * 12)

8x = 360

Divide both sides by 8:

x = 45

Therefore, the height of the pine tree is 45 feet.