Question

solve for ( x ). round to the nearest tenth of a degree, if necessary.
right triangle uvw with right angle at v, uv = 6.1, vw = 3.2, angle at w is ( x^circ )
answer attempt 2 out of 2
( x = ) input box ( ^circ ) submit answer

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( UVW \) (right-angled at \( V \)), we have opposite side to \( x \) as \( UV = 6.1 \) and adjacent side as \( VW = 3.2 \). So we use the tangent function: \( \tan(x)=\frac{\text{opposite}}{\text{adjacent}}=\frac{UV}{VW}=\frac{6.1}{3.2} \)

Step2: Calculate \( x \)

First, compute \( \frac{6.1}{3.2}\approx1.90625 \). Then, take the arctangent (inverse tangent) of \( 1.90625 \): \( x = \arctan(1.90625) \). Using a calculator, \( x\approx62.4^\circ \) (rounded to the nearest tenth of a degree)

Answer:

\( 62.4 \)