Question

solve for ( x ). round to the nearest tenth, if necessary.
(image of a right triangle ( \triangle mno ) with right angle at ( n ), ( on = 6.8 ), ( angle m = 29^circ ), and ( mn = x ))
answer attempt 1 out of 2
( x = ) input box submit answer

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( \triangle MNO \), \( \angle M = 29^\circ \), opposite side to \( \angle M \) is \( ON = 6.8 \), adjacent side is \( MN = x \). We use tangent: \( \tan(\theta)=\frac{\text{opposite}}{\text{adjacent}} \).
So \( \tan(29^\circ)=\frac{6.8}{x} \).

Step2: Solve for \( x \)

Rearrange the formula: \( x = \frac{6.8}{\tan(29^\circ)} \).
Calculate \( \tan(29^\circ) \approx 0.5543 \).
Then \( x \approx \frac{6.8}{0.5543} \approx 12.3 \).

Answer:

\( 12.3 \)