Question

Create a sketch to help you visualize the problem. How tall is Harold?

A) 3 feet
B) 6 feet
C) 9 feet
D) 12 feet

Answer 1

The sketch helps visualize the problem where Harold's height is approximately 9 feet, calculated using the proportion
`\(H/S = V/V_{\text{shadow}}\)` with given shadow lengths. Therefore, the correct answer is C) 9 feet.

Step-by-step explanation:

Creating a sketch is a crucial step in visualizing and solving geometric problems. In this case, let's imagine a scenario where Harold is standing beside a vertical object, like a pole or a tree. If the length of Harold's shadow is 6 feet and the shadow of the vertical object is 4 feet, we can set up a proportion to find Harold's height.

Using the properties of similar triangles, we can express the ratio of Harold's height (H) to his shadow length (S) as equal to the ratio of the height of the vertical object (V) to its shadow length (V_shadow). Mathematically, this relationship is represented as:

`\[ (H)/(S) = \frac{V}{V_{\text{shadow}}} \]`

Substituting the given values, we get:

`\[ (H)/(6) = (V)/(4) \]`

Solving for Harold's height (H), we find:

`\[ H = (V)/(4) * 6 \]`

Now, if we assume that the vertical object's height (V) is 6 feet, then:

`\[ H = (6)/(4) * 6 = 9 \]`

Therefore, based on this proportion, Harold's height is 9 feet. The sketch aids in understanding the geometric relationships and visually confirming the solution.