23. Spatis When Alonzo, who is $$ 5^{\prime} 11^{\prime \prime} $$ tall, stands next to a basketball goal, his shadow is $$ 2^{\prime} $$ 'ong, and the basketball goal's shadow is $$ 4^{\prime} 4^{\prime \prime} $$ long. About how tall is the basketbail goal?

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To solve the problem, we can use the concept of similar triangles. The height of Alonzo and the length of his shadow form one triangle, while the height of the basketball goal and the length of its shadow form another triangle.

### Known Conditions:
1. Alonzo's height: $$ 5' 11'' $$
2. Alonzo's shadow length: $$ 2' $$
3. Basketball goal's shadow length: $$ 4' 4'' $$

### Step 1: Convert heights and lengths to a single unit (inches)
- Alonzo's height in inches:
  $$
  5' 11'' = 5 \times 12 + 11 = 60 + 11 = 71 \text{ inches}
  $$
- Alonzo's shadow length in inches:
  $$
  2' = 2 \times 12 = 24 \text{ inches}
  $$
- Basketball goal's shadow length in inches:
  $$
  4' 4'' = 4 \times 12 + 4 = 48 + 4 = 52 \text{ inches}
  $$

### Step 2: Set up the proportion using similar triangles
Let $$ h $$ be the height of the basketball goal in inches. The proportion based on similar triangles is:
$$
\frac{\text{Height of Alonzo}}{\text{Length of Alonzo's shadow}} = \frac{\text{Height of basketball goal}}{\text{Length of basketball goal's shadow}}
$$
This can be written as:
$$
\frac{71}{24} = \frac{h}{52}
$$

### Step 3: Solve for $$ h $$
Cross-multiplying gives:
$$
71 \times 52 = 24 \times h
$$
Calculating $$ 71 \times 52 $$:
$$
71 \times 52 = 3692
$$
So we have:
$$
3692 = 24h
$$
Now, divide both sides by 24 to find $$ h $$:
$$
h = \frac{3692}{24}
$$

### Step 4: Calculate $$ h $$
Now, let's perform the division:
$$
h = 153.8333 \text{ inches}
$$

### Step 5: Convert $$ h $$ back to feet and inches
To convert inches back to feet and inches:
- Feet: $$ \lfloor \frac{153.8333}{12} \rfloor = 12 $$ feet
- Remaining inches: $$ 153.8333 - (12 \times 12) = 153.8333 - 144 = 9.8333 $$ inches

Thus, the height of the basketball goal is approximately $$ 12' 10'' $$.

### Final Answer:
The basketball goal is about $$ 12' 10'' $$ tall.
The basketball goal is about 12 feet 10 inches tall.

23. Spatis When Alonzo, who is \( 5^{\prime} 11^{\prime \prime} \) tall, stands next to a basketball goal, his shadow is \( 2^{\prime} \) 'ong, and the basketball goal's shadow is \( 4^{\prime} 4^{\prime \prime} \) long. About how tall is the basketbail goal?

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