Question
Use the diagram given to answer the question.
13
32°
What equation can be used to find the value of x in the triangle?
cos(58°)
A.X=
13
B. x = 13 cos(58°)
sin (58°)
C. x=
13
• D. x = 13 sin (58°)
13
32°
What equation can be used to find the value of x in the triangle?
cos(58°)
A.X=
13
B. x = 13 cos(58°)
sin (58°)
C. x=
13
• D. x = 13 sin (58°)
Answers
Answered by
GPT-4o mini
In a triangle, if you are given one side and the angle opposite to that side, you can use trigonometric ratios to find the unknown side (x in this case).
Given the angle \(32^\circ\) and the side \(13\), and looking at the angle \(58^\circ\) (which is the angle at the other vertex since the angles in a triangle sum to \(180^\circ\)), you can use the sine or cosine functions based on the relationship between the angles and sides of the triangle.
The correct option for finding \(x\) using the cosine function is based on the adjacent side and the hypotenuse.
1. If you want to find \(x\) (which is opposite the angle \(58^\circ\)), you would actually use the sine function:
\[ \sin(58^\circ) = \frac{x}{13} \]
This leads to:
\[ x = 13 \sin(58^\circ) \]
So, the correct answer is:
**D. \( x = 13 \sin(58^\circ) \)**
Given the angle \(32^\circ\) and the side \(13\), and looking at the angle \(58^\circ\) (which is the angle at the other vertex since the angles in a triangle sum to \(180^\circ\)), you can use the sine or cosine functions based on the relationship between the angles and sides of the triangle.
The correct option for finding \(x\) using the cosine function is based on the adjacent side and the hypotenuse.
1. If you want to find \(x\) (which is opposite the angle \(58^\circ\)), you would actually use the sine function:
\[ \sin(58^\circ) = \frac{x}{13} \]
This leads to:
\[ x = 13 \sin(58^\circ) \]
So, the correct answer is:
**D. \( x = 13 \sin(58^\circ) \)**