Question

solve for x. round to the nearest tenth, if necessary.
right triangle mln with right angle at m, length of mn is 7.4, angle at l is 23 degrees, length of ml is x
answer attempt 1 out of 2
x = blank submit answer

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( MLN \), \( \angle L = 23^\circ \), opposite side to \( \angle L \) is \( MN = 7.4 \), adjacent side is \( ML = x \). We use tangent: \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \), so \( \tan(23^\circ)=\frac{7.4}{x} \).

Step2: Solve for \( x \)

Rearrange the formula: \( x = \frac{7.4}{\tan(23^\circ)} \). Calculate \( \tan(23^\circ)\approx0.4245 \), then \( x=\frac{7.4}{0.4245}\approx17.4 \).

Answer:

\( 17.4 \)