Anelectric pylon stand on horizontal ground at a point som from the base of the pylon, the angle of elavation of the top of is $$ 23^{\circ} $$ Calculate the height of the pylon

Question

UpStudy AI · Accepted Answer

It looks like you're trying to determine the height of an electric pylon using trigonometry. Let's clarify and solve the problem step by step.

### Given:
- **Angle of Elevation (θ):** $$23^{\circ}$$
- **Distance from the observer to the base of the pylon (s):** Let's assume this is given as "s" meters.

### Objective:
Calculate the **height (h)** of the pylon.

### Diagram:
```
        |
        | h
        |
        |________
           s
```

### Solution:

1. **Understand the Right Triangle:**
   
   The scenario forms a right-angled triangle where:
   - **h** is the side opposite the angle $$23^{\circ}$$.
   - **s** is the adjacent side to the angle $$23^{\circ}$$.

2. **Use Trigonometric Ratios:**
   
   The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side.
   
   $$
   \tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{h}{s}
   $$
   
   Plugging in the known values:
   
   $$
   \tan(23^{\circ}) = \frac{h}{s}
   $$

3. **Solve for Height (h):**
   
   Multiply both sides by $$s$$ to isolate $$h$$:
   
   $$
   h = s \times \tan(23^{\circ})
   $$
   
   $$
   h = s \times 0.4245 \quad (\text{Using} \ \tan(23^{\circ}) \approx 0.4245)
   $$
   
   $$
   h \approx 0.4245s
   $$
   
### Final Answer:

The height of the pylon is approximately **0.4245 times the distance** from the observer to the base.

$$
\boxed{h = s \cdot \tan(23^{\circ})}
$$

### Example:

If the distance $$s$$ is **10 meters**:
   
$$
h = 10 \times 0.4245 = 4.245 \ \text{meters}
$$

So, the pylon would be approximately **4.245 meters** tall.

---

**Note:** To find a numerical value for the height, you'll need to know the specific distance $$s$$ from the observer to the base of the pylon.
The height of the pylon is approximately $$0.4245$$ times the distance from the observer to the base.

Anelectric pylon stand on horizontal ground at a point som from the base of the pylon, the angle of elavation of the top of is \( 23^{\circ} \) Calculate the height of the pylon

Solución de tutoría real

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Trigonometry Questions