a 5 foot vertical pole casts a 3 foot shadow a tree casts a 20 foot shadow. find the height of the tree to the nearest tenth

Question

2nd semester 

dont know where to start

 

Answer 1

This is a proportion problem.  We will use the ratio of object height to shadow length.

For the pole, the ratio is 5 ft:3 ft.

Since the height of the tree is unknown, we will use x for the height of the tree.  The tree height to shadow length ratio is x:20 ft.

Since both ratios are object height: shadow length, we can right a proportion where the ratios are fractions equal to each other.

5/3 = x/20

Cross multiplying (multiply each numerator by the denominator on the other side of the equal sign) produces:

100 = 3x

If we divide each side by 3, we have 33 1/3 ft.

Rounded to the nearest tenth, the answer is 33.3 ft.

 

 

Answer 2

This problem can be solved using a proportion since it has 3 known values and 1 unknown value. It helps to draw a quick diagram for a problem like this labeling the pole 5 ft and its shadow 3 ft, the tree x ft and its shadow 20 ft. Set up the proportion keeping the object's height with its shadow's length together in the proportion: 5ft pole/3ft shadow = xft tree/20ft shadow. Then to solve proportions you just multiply the diagonal numbers and divide by the number diagonal from the unknown. So you would multiply 5(20) and then divide by 3. You would get 100/3 = 33.3 ft (rounded to nearest tenth).

Answer 3

Hi Kayla. This is a simple problem about proportions. First, look at what you know. You know that a vertical pole that is 5 feet tall casts a 3 foot shadow and a tree that has an unknown height casts a 20 foot shadow. So we want to know the height of the tree. To do this we set up a proportion, which is a statement that shows that two ratios are equal even if the actual numbers differ. You can write them as fractions or as ratios( with a colon).

 

They look like this:

3/4=6/8(fraction form) or

3:4=6:8(ratio form)

I find its easier to use fractions.

So in this case, lets first write our fraction bars and equal sign. Set up the equation without the numbers.

1.  / = /

Now we need to fill in the numbers that we know. We already know one of the fractions which is the 5 foot pole and its 3 foot shadow. You can put either number in the numerator and denominator of one of the fractions, but the second fractions' values must correspond with the first fraction. For example, with this , I'm going to put the vertical heights ( of the pole and the tree) in the numerators and the shadows (of both) in the denominators. We can write "x" in place off the unknown height of the tree.So far we have this:

2. 5/3=  x/20

Then you multiply the numbers diagonally and place the answers on each side of the equal sign . It doesn't matter which side you multiply first.

3. 20*5=100 and 3*x=3x

100=3x

Now you want to get the "x" by itself. To do this we need to divide it by 3. But, whatever you do to one side , you have to do to the other side. So you have to divide 100 by 3 as well.

4. 33.3333=x

So, now we know that our x is equal to 33.3333. We said earlier that we were using x to stand for the height of tree. So that means that the tree is 33.3333 feet tall. The question said find the height of the tree to the nearest tenth. This means we have to shorten our answer to 33.3.

 

This means that the height of the tree is 33.3.