Question

find m∠v.
(image of a right triangle with right angle at w, leg xw = 4.1, leg wv = 6.4, vertices x, w, v. w has a right angle symbol. write your answer as an integer or as a decimal rounded to the nearest tenth. m∠v = °)

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( \triangle VWX \), \( \angle W = 90^\circ \), \( WX = 4.1 \) (opposite to \( \angle V \)), \( WV = 6.4 \) (adjacent to \( \angle V \)). We use the tangent function: \( \tan(V) = \frac{\text{opposite}}{\text{adjacent}} = \frac{WX}{WV} \).

Step2: Calculate \( \tan(V) \)

Substitute values: \( \tan(V) = \frac{4.1}{6.4} \approx 0.6406 \).

Step3: Find \( \angle V \)

Take the arctangent: \( V = \arctan(0.6406) \approx 32.6^\circ \).

Answer:

\( 32.6 \)