A lamp post that is 8 ft high casts a shadow 5 ft long. How tall is the person standing beside the lamp post if his shadow is 3.5 ft long?
since the ratio of height:shadow is the same,
8/5 = x/3.5
8/5 = h/3.5
To solve this problem, we can set up a proportion using the similar triangles formed by the lamp post and its shadow, as well as the person and their shadow.
Let's use the following ratios:
Height of the lamp post / Length of the lamp post's shadow = Height of the person / Length of the person's shadow
Now we can substitute the given values:
8 ft / 5 ft = Height of the person / 3.5 ft
To solve for the height of the person, we can cross-multiply and divide:
(8 ft * 3.5 ft) / 5 ft = Height of the person
Multiplying the values:
28 ft-ft / 5 ft = Height of the person
Simplifying:
5.6 ft = Height of the person
Therefore, the person standing beside the lamp post is approximately 5.6 ft tall.
To find the height of the person standing beside the lamp post, we can use a proportion. The proportion relates the height of the lamp post to the length of its shadow and the height of the person to the length of their shadow.
Let's set up the proportion:
Height of the lamp post / Length of its shadow = Height of the person / Length of their shadow
Plugging in the given values:
8 ft / 5 ft = Height of the person / 3.5 ft
To solve for the height of the person, we need to isolate the variable. Cross-multiply the proportion:
8 ft * 3.5 ft = 5 ft * Height of the person
28 ft² = 5 ft * Height of the person
Now, divide both sides of the equation by 5 ft to solve for the Height of the person:
28 ft² / 5 ft = Height of the person
The unit "ft" in the numerator cancels out with "ft" in the denominator, leaving us with just "ft" as the unit of height:
5.6 ft = Height of the person
Therefore, the person standing beside the lamp post is approximately 5.6 feet tall.