Kurt spots a bird sitting at the top of a 40 foot tall telephone pole. If
the angle of elevation from the ground where he is standing to the
bird is , how far is Kurt standing from the base of the pole?

Question

Kurt spots a bird sitting at the top of a 40 foot tall telephone pole. If
the angle of elevation from the ground where he is standing to the
bird is

, how far is Kurt standing from the base of the pole?

UpStudy AI · Accepted Answer

To determine how far Kurt is standing from the base of the telephone pole, we can use trigonometry, specifically the tangent function in a right triangle.

### Given:
- **Height of the pole (Opposite side):** 40 feet
- **Angle of elevation (θ):** $$ 59^\circ $$
- **Distance from the base (Adjacent side):** $$ x $$ feet (what we need to find)

### Using the Tangent Function:
The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side:
$$
\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}
$$
Plugging in the known values:
$$
\tan(59^\circ) = \frac{40}{x}
$$
Solving for $$ x $$:
$$
x = \frac{40}{\tan(59^\circ)}
$$

### Calculating $$ \tan(59^\circ) $$:
Using a calculator:
$$
\tan(59^\circ) \approx 1.6643
$$

### Finding $$ x $$:
$$
x = \frac{40}{1.6643} \approx 24.07 \text{ feet}
$$

### Rounding:
Depending on the desired precision, you can round this to:
$$
x \approx 24.0 \text{ feet}
$$

### **Final Answer:**
Kurt is approximately 24.0 feet from the base of the telephone pole.
Kurt is approximately 24.0 feet from the base of the telephone pole.

Kurt spots a bird sitting at the top of a 40 foot tall telephone pole. If
the angle of elevation from the ground where he is standing to the
bird is , how far is Kurt standing from the base of the pole?

Solución de inteligencia artificial de Upstudy

Responder

Solución

Given:

Using the Tangent Function:

Calculating :

Finding :

Rounding:

Final Answer:

The Deep Dive

preguntas relacionadas

Latest Trigonometry Questions

Kurt spots a bird sitting at the top of a 40 foot tall telephone pole. If the angle of elevation from the ground where he is standing to the bird is , how far is Kurt standing from the base of the pole?

Solución de inteligencia artificial de Upstudy

Responder

Solución

Given:

Using the Tangent Function:

Calculating :

Finding :

Rounding:

Final Answer:

The Deep Dive

preguntas relacionadas

Latest Trigonometry Questions

Kurt spots a bird sitting at the top of a 40 foot tall telephone pole. If
the angle of elevation from the ground where he is standing to the
bird is , how far is Kurt standing from the base of the pole?