Question

solve for x. round to the nearest tenth.

Explanation:

Step1: Identify the triangle type and trigonometric ratio

This is a right - triangle. We know the hypotenuse \( c = 28 \) and we want to find the side \( x \) which is adjacent to the \( 46^{\circ} \) angle. The cosine of an angle in a right - triangle is defined as \( \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}} \). So, \( \cos(46^{\circ})=\frac{x}{28} \).

Step2: Solve for \( x \)

To solve for \( x \), we can multiply both sides of the equation by 28: \( x = 28\times\cos(46^{\circ}) \).
We know that \( \cos(46^{\circ})\approx0.6947 \).
Then \( x = 28\times0.6947\approx19.4516 \). Rounding to the nearest tenth, we get \( x\approx19.5 \).

Answer:

\( 19.5 \)