Question

solve for x. round to the nearest tenth, if necessary.
answer attempt 1 out of 3
x =

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( LMN \) (right - angled at \( M \)), we know an angle \( \angle N = 46^{\circ} \), the hypotenuse \( LN = 4.1 \), and we need to find the adjacent side \( x = MN \) to the angle \( \angle N \). The cosine of an angle in a right triangle is defined as the ratio of the adjacent side to the hypotenuse. So, \( \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}} \), where \( \theta = 46^{\circ} \), adjacent side is \( x \), and hypotenuse is \( 4.1 \). So, \( \cos(46^{\circ})=\frac{x}{4.1} \).

Step2: Solve for \( x \)

To solve for \( x \), we can multiply both sides of the equation \( \cos(46^{\circ})=\frac{x}{4.1} \) by \( 4.1 \). So, \( x = 4.1\times\cos(46^{\circ}) \). We know that \( \cos(46^{\circ})\approx0.6947 \). Then \( x = 4.1\times0.6947 \approx 2.848 \). Rounding to the nearest tenth, we get \( x\approx2.8 \).

Answer:

\( x\approx2.8 \)