Question

standard 14 homework
score: 6/30 answered: 5/18
question 6
suppose ( c = 7 ) and ( a = 10 ^ { circ } ) in the right triangle shown above. find each of the following values. round
your answers to one decimal place.
( a = )
( b = )
( b = ) degrees
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Explanation:

Step1: Find angle \( B \)

In a right - triangle, the sum of angles is \( 180^{\circ} \). Since one angle is \( 90^{\circ} \) and \( A = 10^{\circ} \), then \( B=180^{\circ}-90^{\circ}-10^{\circ}=80^{\circ} \)

Step2: Find side \( a \)

Using the sine function \( \sin A=\frac{a}{c} \). Given \( c = 7 \) and \( A = 10^{\circ} \), then \( a=c\sin A \). Substitute the values: \( a = 7\times\sin(10^{\circ})\). Since \( \sin(10^{\circ})\approx0.1736 \), \( a=7\times0.1736 = 1.2152\approx1.2 \)

Step3: Find side \( b \)

Using the cosine function \( \cos A=\frac{b}{c} \). Given \( c = 7 \) and \( A = 10^{\circ} \), then \( b=c\cos A \). Substitute the values: \( b = 7\times\cos(10^{\circ})\). Since \( \cos(10^{\circ})\approx0.9848 \), \( b=7\times0.9848=6.8936\approx6.9 \)

Answer:

\( a = 1.2 \), \( b = 6.9 \), \( B = 80.0 \) degrees