Logan and Maisie are stood on
opposite sides of a phone mast. The
phone mast is 120 m tall.
The angle of elevation from Logan to
the top of the mast is .
The angle of elevation from Maisie tc
the top of the mast is .

Ask by Bowman Zimmerman. in the United Kingdom

Jan 31,2025

Question

Logan and Maisie are stood on
opposite sides of a phone mast. The
phone mast is 120 m tall.
The angle of elevation from Logan to
the top of the mast is .
The angle of elevation from Maisie tc
the top of the mast is .

Ask by Bowman Zimmerman. in the United Kingdom

Jan 31,2025

UpStudy AI · Accepted Answer

To determine the distance between Logan and Maisie, we'll analyze the given information using trigonometry. Here's a step-by-step solution:

### **Given:**
- **Height of the phone mast (h):** 120 meters
- **Angle of elevation from Logan to the top of the mast (θ₁):** 68°
- **Angle of elevation from Maisie to the top of the mast (θ₂):** 42°

### **Objective:**
Find the distance between Logan and Maisie.

### **Assumptions:**
- Logan and Maisie are standing on **opposite sides** of the phone mast.
- The ground is level.

### **Steps:**

1. **Determine the Distance from Logan to the Mast (x):**

- Using the tangent of the angle of elevation:
     $$
     \tan(\theta₁) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{h}{x}
     $$
     $$
     x = \frac{h}{\tan(\theta₁)} = \frac{120}{\tan(68°)}
     $$
     
   - Calculate $$\tan(68°)$$:
     $$
     \tan(68°) \approx 2.4751
     $$
     
   - Calculate $$x$$:
     $$
     x \approx \frac{120}{2.4751} \approx 48.48 \text{ meters}
     $$

2. **Determine the Distance from Maisie to the Mast (y):**

- Using the tangent of the angle of elevation:
     $$
     \tan(\theta₂) = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{h}{y}
     $$
     $$
     y = \frac{h}{\tan(\theta₂)} = \frac{120}{\tan(42°)}
     $$
     
   - Calculate $$\tan(42°)$$:
     $$
     \tan(42°) \approx 0.9004
     $$
     
   - Calculate $$y$$:
     $$
     y \approx \frac{120}{0.9004} \approx 133.27 \text{ meters}
     $$

3. **Calculate the Total Distance Between Logan and Maisie:**

- Since Logan and Maisie are on opposite sides of the mast, the total distance ($$D$$) between them is the sum of $$x$$ and $$y$$:
     $$
     D = x + y \approx 48.48 \text{ m} + 133.27 \text{ m} = 181.75 \text{ meters}
     $$

### **Conclusion:**
The distance between Logan and Maisie is approximately **181.75 meters**.

Rounded to a practical value:
$$
D \approx 182 \text{ meters}
$$
The distance between Logan and Maisie is approximately 182 meters.

Logan and Maisie are stood on
opposite sides of a phone mast. The
phone mast is 120 m tall.
The angle of elevation from Logan to
the top of the mast is .
The angle of elevation from Maisie tc
the top of the mast is .

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Solución

Given:

Objective:

Assumptions:

Steps:

Conclusion:

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Latest Trigonometry Questions

Logan and Maisie are stood on opposite sides of a phone mast. The phone mast is 120 m tall. The angle of elevation from Logan to the top of the mast is . The angle of elevation from Maisie tc the top of the mast is .

Solución de inteligencia artificial de Upstudy

Responder

Solución

Given:

Objective:

Assumptions:

Steps:

Conclusion:

Extra Insights

preguntas relacionadas

Latest Trigonometry Questions

Logan and Maisie are stood on
opposite sides of a phone mast. The
phone mast is 120 m tall.
The angle of elevation from Logan to
the top of the mast is .
The angle of elevation from Maisie tc
the top of the mast is .