Question

At 3:00 PM a man 135 cm tall casts a shadow 150 cm long. At the same time, a tall building nearby casts a shadow 171 m long. How tall is the building?

Answer 1

I can help you solve this problem using similar triangles. Here are the steps and the results:

- To find the height of the building, we need to use the fact that the ratio of the height to the shadow length is the same for both the man and the building, because they are under the same angle of sunlight. This means that we can set up a proportion and cross-multiply to find the unknown value. Using the formula from [this website], we can write:

h / 171 = 135 / 150

- To solve for h, we need to multiply both sides by 171 and simplify. We get:

h = 171 * 135 / 150

h = 153.9

- Therefore, the height of the building is **153.9 m**. This is the answer to the problem. I hope this helps you understand how to use similar triangles to find missing lengths. If you have any questions, please let me know.

Answer 2

153.9 meters

Explanation:

Definition:

Proportion: A statement of equality between two ratios.

Ratio: A comparison of two quantities.

Solution:

In order to find the height of the building, we can use the following proportion:

Man's height : Man's shadow = Building's height : Building's shadow

This proportion states that the ratio of the man's height to his shadow is equal to the ratio of the building's height to its shadow.

We know that the man's height is 135 cm and his shadow is 150 cm. Let the height of the building be x.

We also know that the building's shadow is 171 m. We can convert the man's height and shadow to meters by dividing by 100:

`\sf \textsf{Man's height} = (135 cm )/(100) = 1.35 m`

`\sf \textsf{Man's shadow} =( 150 cm )/(100 )= 1.5 m`

Now we can substitute these values into proportion:

1.35 m : 1.5 m = x m : 171 m

This proportion can be rewritten as follows:

`\sf (1.35 m )/( 1.5 m)= (x )/( 171 m)`

Cross-multiplying and solving for x, we get:

`\sf x = (1.35 m )/( 1.5 m)* 171 m`

`\sf x = 153.9 m`

Therefore, the building is 153.9 meters tall.