https://r2.erweima.ai/mathbot/image/17261866423104oxudi8a.jpg

En el hoyo 17 de un campo de golf se debe atravesar un pequeño lago. Para determinar la longitud que debe recorrer la pelota desde el punto A hasta el punto B, un golfista tomó las siguientes medidas desde el punto C, como se muestra en la ilustración.


La longitud del lago es, aproximadamente:



To determine the approximate length the golf ball needs to travel from point \(A\) to point \(B\) across the lake, we can use the Law of Cosines. The triangle formed by points \(A\), \(B\), and \(C\) is a non-right triangle, so the Law of Cosines will allow us to find the length of side \(AB\).

### Given:
- \(AC = 37.8 \, \text{m}\)
- \(BC = 23.7 \, \text{m}\)
- \(\delta = 54^\circ\) (angle at point \(C\))

### Formula: Law of Cosines
\[
AB^2 = AC^2 + BC^2 - 2 \cdot AC \cdot BC \cdot \cos(\delta)
\]

### Calculations:
Let's calculate the length of \(AB\):

\[
AB = \sqrt{37.8^2 + 23.7^2 - 2 \cdot 37.8 \cdot 23.7 \cdot \cos(54^\circ)}
\]

I'll compute this for you.The approximate length of the lake that the golf ball must travel from point \(A\) to point \(B\) is **30.6 meters**.

Would you like more details or have any questions? Here are some related questions you might consider:

1. How can the Law of Cosines be used to solve different types of triangle problems?
2. What are the differences between the Law of Sines and the Law of Cosines?
3. How would you find the length of the lake if you had a different set of angles?
4. How can trigonometric laws be applied to real-world navigation problems?
5. What would change if the angle \(\delta\) was an obtuse angle?

**Tip:** Remember that in non-right triangles, the Law of Cosines is helpful to find unknown sides or angles when two sides and the included angle are known.

En el hoyo 17 de un campo de golf se debe atravesar un pequeño lago. Para determinar la longitud que debe recorrer la pelota desde el punto A hasta el punto B, un golfista tomó las siguientes medidas desde el punto C, como se muestra en la ilustración. La longitud del lago es, aproximadamente:

Learn how to calculate the length of a golf shot across a lake by applying the Law of Cosines. In this problem, points A, B, and C form a triangle, with AC = 37.8 m, BC = 23.7 m, and an included angle of 54°. The solution demonstrates the use of trigonometric formulas to find the length of the shot, approximately 30.6 meters.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation