At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
To solve this problem, we need to use the appropriate trigonometric ratio based on the given angle and the length of the board.
Given:
- The length of the board \( AB \) is 10 feet.
- The angle \( \theta \) between the board and the ground is \( 60^\circ \).
We need to find the horizontal distance \( x \) from the base of the board to the wall (point \( A \) to the wall at point \( C \)). This scenario forms a right triangle \( ABC \) where:
- \( AC \) (the distance we need to find) is the adjacent side of the angle \( 60^\circ \).
- \( AB \) (the length of the board) is the hypotenuse.
The cosine function relates the adjacent side to the hypotenuse in a right triangle. Specifically,
[tex]\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \][/tex]
Using the given values:
[tex]\[ \cos(60^\circ) = \frac{x}{10} \][/tex]
We know that \( \cos(60^\circ) \) is \( \frac{1}{2} \). Hence,
[tex]\[ \frac{1}{2} = \frac{x}{10} \][/tex]
To solve for \( x \), we multiply both sides by 10:
[tex]\[ x = 10 \times \frac{1}{2} \][/tex]
[tex]\[ x = 5 \][/tex]
Therefore, the base of the board (point \( A \)) is 5 feet away from the wall (point \( C \)).
The correct trig ratio and distance from the wall, according to the choices given, is:
C. [tex]\(\cos 60^\circ = \frac{x}{10} ; x=5\)[/tex] feet
Given:
- The length of the board \( AB \) is 10 feet.
- The angle \( \theta \) between the board and the ground is \( 60^\circ \).
We need to find the horizontal distance \( x \) from the base of the board to the wall (point \( A \) to the wall at point \( C \)). This scenario forms a right triangle \( ABC \) where:
- \( AC \) (the distance we need to find) is the adjacent side of the angle \( 60^\circ \).
- \( AB \) (the length of the board) is the hypotenuse.
The cosine function relates the adjacent side to the hypotenuse in a right triangle. Specifically,
[tex]\[ \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \][/tex]
Using the given values:
[tex]\[ \cos(60^\circ) = \frac{x}{10} \][/tex]
We know that \( \cos(60^\circ) \) is \( \frac{1}{2} \). Hence,
[tex]\[ \frac{1}{2} = \frac{x}{10} \][/tex]
To solve for \( x \), we multiply both sides by 10:
[tex]\[ x = 10 \times \frac{1}{2} \][/tex]
[tex]\[ x = 5 \][/tex]
Therefore, the base of the board (point \( A \)) is 5 feet away from the wall (point \( C \)).
The correct trig ratio and distance from the wall, according to the choices given, is:
C. [tex]\(\cos 60^\circ = \frac{x}{10} ; x=5\)[/tex] feet
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.