4. CONSTRUCTION A roofer props a ladder against a wall so that the top of the ladder reaches a 30 -foot roof that needs repair. If the angle of elevation from the bottom of the ladder to the roof is $$ 55^{\circ} $$, how far is the ladder from the base of the wall? Round your answer to the nearest foot.

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**Step 1: Identify the right triangle components**  
The ladder, wall, and ground form a right triangle. The height of the roof is the side opposite the $$55^\circ$$ angle, and the distance from the ladder to the wall is the side adjacent to the angle.

**Step 2: Use the tangent function**  
In a right triangle, the tangent of an angle is the ratio of the opposite side to the adjacent side. Therefore,  
$$
\tan(55^\circ) = \frac{30}{x}
$$  
where $$x$$ is the horizontal distance from the base of the wall to the ladder.

**Step 3: Solve for $$x$$**  
Rearrange the equation to solve for $$x$$:  
$$
x = \frac{30}{\tan(55^\circ)}
$$

**Step 4: Calculate $$x$$**  
First, compute $$\tan(55^\circ)$$. Using a calculator,  
$$
\tan(55^\circ) \approx 1.4281
$$

Then,  
$$
x \approx \frac{30}{1.4281} \approx 21
$$

**Step 5: Round the answer**  
Since the problem asks for the answer rounded to the nearest foot,  
$$
x \approx 21 \text{ feet}
$$

**Final Answer:** $$21$$ feet.
The ladder is approximately 21 feet away from the base of the wall.

CONSTRUCTION A roofer props a ladder against a wall so that the top of the ladder reaches a 30 -foot roof that needs
repair. If the angle of elevation from the bottom of the ladder to the roof is , how far is the ladder from the base of
the wall? Round your answer to the nearest foot.

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CONSTRUCTION A roofer props a ladder against a wall so that the top of the ladder reaches a 30 -foot roof that needs repair. If the angle of elevation from the bottom of the ladder to the roof is , how far is the ladder from the base of the wall? Round your answer to the nearest foot.