Question

1. solve the following triangles. if needed, round your answers to one decimal place.

a.
step 1: find angle b.
we know
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step 2: find c.
we know
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step 3: find b.
we know
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Explanation:

Step1: Find angle \( B \)

Sum of angles in a triangle is \( 180^{\circ} \).
Since it is a right - triangle (\( 90^{\circ}\) angle), \( B=180^{\circ}-90^{\circ}-40^{\circ}=50^{\circ}\)

Step2: Find \( c \)

Using cosine function: \( \cos40^{\circ}=\frac{25}{c}\)
\( c=\frac{25}{\cos40^{\circ}}\approx\frac{25}{0.766}\approx32.6\) cm

Step3: Find \( b \)

Using tangent function: \( \tan40^{\circ}=\frac{b}{25}\)
\( b = 25\times\tan40^{\circ}\approx25\times0.839\approx21.0\) cm

Answer:

Angle \( B = 50^{\circ}\), \( c\approx32.6\) cm, \( b\approx21.0\) cm