Question

question
in δwxy, y = 940 inches, m∠y = 100°, and m∠w = 38°. find the length of w, to the nearest inch.
answer attempt 1 out of 5
w =
inches
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Explanation:

Step1: Find angle at X

In triangle \( \triangle WXY \), the sum of interior angles is \( 180^\circ \). So \( m\angle X = 180^\circ - m\angle Y - m\angle W = 180^\circ - 100^\circ - 38^\circ = 42^\circ \).

Step2: Apply Law of Sines

The Law of Sines states \( \frac{w}{\sin m\angle Y} = \frac{y}{\sin m\angle X} \). We know \( y = 940 \), \( m\angle Y = 100^\circ \), \( m\angle X = 42^\circ \). So \( w = \frac{y \cdot \sin m\angle Y}{\sin m\angle X} \).

Step3: Calculate the values

First, find \( \sin 100^\circ \approx 0.9848 \) and \( \sin 42^\circ \approx 0.6691 \). Then \( w = \frac{940 \cdot 0.9848}{0.6691} \approx \frac{925.712}{0.6691} \approx 1383.5 \). Rounding to the nearest inch, \( w \approx 1384 \).

Answer:

\( 1384 \)