Question

A vertical pole is held in position by a wire 5m long. The wire slopes at 62° to the horizontal. Find the distance from the foot of the pole to the point where the wire is fixed to the ground

Answer 1

To find the distance from the foot of the pole to the point where the wire is fixed to the ground, we can use some basic trigonometry.

### Given:
- Length of the wire (hypotenuse, \( L \)) = 5 m
- Angle of the wire with the horizontal (\( \theta \)) = 62°

### Required:
- Distance from the foot of the pole to the point where the wire is fixed on the ground (adjacent side of the triangle, \( d \)).

### Using the cosine function:
The cosine of the angle in a right triangle is given by:

\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]

For our problem:

\[
\cos(62°) = \frac{d}{5}
\]

To find \( d \):

\[
d = 5 \cdot \cos(62°)
\]

### Calculate \( \cos(62°) \):
Using a calculator:

\[
\cos(62°) \approx 0.4695
\]

### Substitute into the equation for \( d \):
\[
d = 5 \cdot 0.4695 \approx 2.3475 \text{ m}
\]

### Final Answer:
The distance from the foot of the pole to the point where the wire is fixed to the ground is approximately **2.35 meters**.