https://file.aiquickdraw.com/mathbot/file/1728207511512x0igh7mk.jpg

We can solve this problem using trigonometry, as we are dealing with a right triangle formed by the tent pole, the ground, and the wire.

### Known Values:
- The length of the wire (hypotenuse of the triangle) = 51 feet.
- The angle between the wire and the ground = 56°.
- The height of the tent pole (opposite side) = 44 feet.

### Steps:
1. **Find the horizontal distance (adjacent side)** between the bottom of the tent pole and the point where the wire touches the ground.

We can use the sine function, since \(\sin(\theta) = \frac{{\text{{opposite}}}}{{\text{{hypotenuse}}}}\):
\[
\sin(56^\circ) = \frac{44}{51}
\]
From this, we can verify if the hypotenuse length satisfies the equation, then proceed to find the adjacent side using cosine.

2. **Find the adjacent side** (horizontal distance) using the cosine function:
\[
\cos(56^\circ) = \frac{{\text{{adjacent}}}}{{51}}
\]
\[
\text{{adjacent}} = 51 \times \cos(56^\circ)
\]

Let me calculate these values for you.The calculated height of the pole based on the sine function is approximately 42 feet, which is slightly off from the given height of 44 feet. This indicates that the provided values might not perfectly match the conditions of a right triangle.

However, based on the given information and using the cosine function, the horizontal distance (adjacent side) between the bottom of the tent pole and the point where the wire is fastened to the ground is approximately **29 feet**.

Would you like more details on this, or do you have any questions?

Here are some related questions to consider:
1. How does adjusting the angle affect the length of the adjacent side?
2. What would be the effect of increasing the length of the wire?
3. How can you determine if the values given form a valid triangle?
4. Can this problem be solved using the Pythagorean theorem, and how would it differ?
5. How could this method be applied to real-world construction problems?

**Tip:** Always verify if the given values are consistent before solving trigonometric problems, as small inaccuracies can affect the solution.

A 51-foot wire running from the top of a tent pole to the ground makes an angle of 56° with the ground. If the length of the tent pole is 44 feet, find the distance from the bottom of the tent pole to the point where the wire is fastened to the ground.

Solve the trigonometry problem involving a 51-foot wire, 44-foot tent pole, and a 56° angle with the ground. Learn how to calculate the horizontal distance using the cosine function. Suitable for Grades 10-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation