Question

question
solve for x. round to the nearest tenth of a degree, if necessary.
(image of a right triangle with right angle at v, vw = 3.2, vu = 6.1, angle at m is x degrees)

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( \triangle UVW \) (right - angled at \( V \)), we know the opposite side (\( UV = 6.1 \)) and the adjacent side (\( VW=3.2 \)) with respect to angle \( x \) at \( W \). The tangent of an angle in a right triangle is defined as the ratio of the opposite side to the adjacent side. So, \( \tan(x)=\frac{\text{opposite}}{\text{adjacent}}=\frac{UV}{VW} \).

Step2: Substitute the values

Substitute \( UV = 6.1 \) and \( VW = 3.2 \) into the tangent formula: \( \tan(x)=\frac{6.1}{3.2}\approx1.90625 \).

Step3: Find the angle \( x \)

To find \( x \), we take the arctangent (inverse tangent) of \( 1.90625 \). So, \( x=\arctan(1.90625) \). Using a calculator, we find that \( x\approx62.4^{\circ} \) (rounded to the nearest tenth of a degree).

Answer:

\( x\approx62.4^{\circ} \)