Question

A man that is 6 feet tall casts a shadow of 9 feet. A building casts a shadow of 36 feet. How tall is the building?

Answer 1

Set up a proportion
6/9 = x/36
Cross multiply
9x = 6(36)
9x = 216
x = 24 ft

Answer 2

Answer: 24 feet tall

Explanation: In this problem, I would first draw a picture of the man and his shadow.

We know that the man is 6 feet tall and that he casts a shadow that is 9 feet.

Next, let;'s draw the picture of the building and its shadow.

We know that the shadow casted by the building is 36 feet and we are asked how tall the building is which means we can use 'x' to represent the height of the building.

Notice that the two triangles that we drew are similar because the both have right angles and the shadows are cast at the same angle. So the triangle are similar by the angle angle similarity postulate.

Remember that if two triangles are similar, the the lengths of the corresponding sides are in proportion.

So, we can set up the proportion 6 is to x as 9 is to 36. It can also be written as followed.

`(6)/(x) = (9)/(36)`

Solving from here, we have 6 × 36 or 216 = 9 multiplied by x or 9x.

216 = 9x

Now, we divide both sides by 9 and we get x = 24.

This means that the building is 24 feet tall.