A wall is to be supported by a wooden pole. In order for a support pole to keep a wall vertical, the
angle of elevation of the pole must be within the range of degrees. If the pole is 8 feet long,
determine the distance from the base of the wall to position the pole.

Question

A wall is to be supported by a wooden pole. In order for a support pole to keep a wall vertical, the
angle of elevation of the pole must be within the range of

degrees. If the pole is 8 feet long,
determine the distance from the base of the wall to position the pole.

UpStudy AI · Accepted Answer

To determine the appropriate distance from the base of the wall to position the 8-foot-long support pole, we can use trigonometry, specifically the cosine function. The angle of elevation ($$\theta$$) of the pole affects the horizontal distance ($$d$$) from the wall. The relationship is given by:

$$
d = \text{length of pole} \times \cos(\theta)
$$

Given:
- Length of the pole ($$L$$) = 8 feet
- Angle of elevation ($$\theta$$) varies between 30° and 60°

Let's calculate the distance for both extreme angles.

1. **At $$\theta = 60^\circ$$:**
   $$
   d = 8 \times \cos(60^\circ) = 8 \times 0.5 = 4 \text{ feet}
   $$

2. **At $$\theta = 30^\circ$$:**
   $$
   d = 8 \times \cos(30^\circ) = 8 \times \left(\frac{\sqrt{3}}{2}\right) = 4\sqrt{3} \text{ feet} \approx 6.93 \text{ feet}
   $$

**Conclusion:**
To ensure the wall remains vertical, the base of the pole should be placed at a distance between **4 feet** and **$$4\sqrt{3}$$ feet** (approximately 6.93 feet) from the wall.

**Final Answer:**
Place the pole so its base is between 4 feet and 4 √3 feet from the wall.
To keep the wall vertical, place the 8-foot pole so its base is between 4 feet and approximately 6.93 feet from the wall.

A wall is to be supported by a wooden pole. In order for a support pole to keep a wall vertical, the
angle of elevation of the pole must be within the range of degrees. If the pole is 8 feet long,
determine the distance from the base of the wall to position the pole.

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A wall is to be supported by a wooden pole. In order for a support pole to keep a wall vertical, the angle of elevation of the pole must be within the range of degrees. If the pole is 8 feet long, determine the distance from the base of the wall to position the pole.

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Latest Trigonometry Questions

A wall is to be supported by a wooden pole. In order for a support pole to keep a wall vertical, the
angle of elevation of the pole must be within the range of degrees. If the pole is 8 feet long,
determine the distance from the base of the wall to position the pole.