Question

find $m\angle w$.

write your answer as an integer or as a decimal rounded to the nearest tenth.
$m\angle w = \square ^\circ$

Explanation:

Step1: Identify sides relative to ∠W

In right triangle \(VWX\) (right-angled at \(V\)):

• Adjacent side to \(∠W\): \(VW = \sqrt{5}\)
• Hypotenuse: \(WX = \sqrt{34}\)

Step2: Use cosine definition

Cosine of \(∠W\) is ratio of adjacent to hypotenuse:
\(\cos(\angle W) = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{\sqrt{5}}{\sqrt{34}}\)

Step3: Calculate inverse cosine

Simplify \(\frac{\sqrt{5}}{\sqrt{34}} \approx \frac{2.236}{5.830} \approx 0.3835\)
Find \(∠W\) using arccosine:
\(\angle W = \arccos(0.3835)\)

Step4: Compute the angle

\(\angle W \approx 67.5^\circ\)

Answer:

\(67.5\)