There is a flag pole that is 12ft tall its shadow is 18 ft long there is a man that is 6 ft standing next to the pole how long is his shadow? How would i figure this out
6 foot height * ( 18 feet shadow / 12 feet height ) = ? feet shadow
thnx!!!
To figure out the length of the man's shadow, you can use the concept of similar triangles. Here's how you can calculate it:
Step 1: Identify the triangles involved.
- The first triangle consists of the flag pole and its shadow.
- The second triangle consists of the man and his shadow.
Step 2: Determine the corresponding sides of the two triangles.
- The height of the flag pole (12 ft) corresponds to the length of its shadow (18 ft).
- The height of the man (6 ft) corresponds to the length of his shadow, which we need to calculate.
Step 3: Set up a proportion.
- Since the ratios of corresponding sides in similar triangles are equal, we can set up a proportion.
- The proportion is: (height of flag pole) / (length of flag pole's shadow) = (height of man) / (length of man's shadow).
Step 4: Substitute the values into the proportion.
- (12 ft) / (18 ft) = (6 ft) / (x ft), where x is the length of the man's shadow.
Step 5: Solve the proportion for x.
- Cross-multiply: 18 ft * (6 ft) = 12 ft * (x ft).
- Simplify: 108 ft = 12 ft * x ft.
- Divide both sides by 12 ft: x ft = 9 ft.
Therefore, the length of the man's shadow is 9 ft.