Question

solve for x. round to the nearest tenth of a degree, if necessary.
(image of right triangle lmn with right angle at m, mn = 4.2, ml = 5.5, angle at n is x degrees)

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( \triangle NML \) (right - angled at \( M \)), for angle \( x \) (at \( N \)), the opposite side to \( x \) is \( ML = 5.5 \) and the adjacent side to \( x \) is \( MN=4.2 \). We use the tangent function, which is defined as \( \tan(x)=\frac{\text{opposite}}{\text{adjacent}} \). So \( \tan(x)=\frac{ML}{MN}=\frac{5.5}{4.2} \).

Step2: Calculate the value of \( \tan(x) \)

\( \frac{5.5}{4.2}\approx1.3095 \)

Step3: Find \( x \) using inverse tangent

To find \( x \), we take the inverse tangent (arctangent) of \( 1.3095 \). So \( x = \arctan(1.3095) \). Using a calculator, \( x\approx52.6^{\circ} \) (rounded to the nearest tenth of a degree).

Answer:

\( x\approx52.6^{\circ} \)