Question

solve for ( x ). round to the nearest tenth, if necessary.

triangle with vertices n, m, l (right angle at m), angle at n is ( 46^circ ), hypotenuse nl = 4.1, side nm = ( x )

answer attempt 1 out of 2
( x = ) input box submit answer

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( \triangle NML \), \( \angle N = 46^\circ \), hypotenuse \( NL = 4.1 \), and \( x = NM \) is adjacent to \( \angle N \). So we use cosine: \( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \).
\( \cos(46^\circ) = \frac{x}{4.1} \)

Step2: Solve for \( x \)

Multiply both sides by \( 4.1 \): \( x = 4.1 \times \cos(46^\circ) \)
Calculate \( \cos(46^\circ) \approx 0.6947 \), then \( x \approx 4.1 \times 0.6947 \approx 2.848 \)
Round to nearest tenth: \( x \approx 2.8 \)

Answer:

\( 2.8 \)