Реши задачу

Дано: \(\triangle{ABC}\) , где \(a = 5\) , \(\angle{B} = 70\degree\) , \(\angle{C} = 80\degree\) .

Найти: \(b\) , \(c\) , \(\angle{A}\) .

Округли значения \(b\) и \(c\) до тысячных.

Решение.

1. \(\angle A = 180\degree-(∠B+∠C)\) (по теореме о сумме углов треугольника), тогда \(∠A=\) [ ] \(\degree\) .

2. По теореме синусов \(\dfrac{a}{\sin A}=\dfrac{b}{\sin B}\) , тогда:

\(b=(a\) [ \(+\) | \(-\) | \(\cdot\) | \(\div\) ][ \(\sin A\) | \(\sin B\) ] \()\) [ \(+\) | \(-\) | \(\cdot\) | \(\div\) ][ \(\sin B\) | \(\sin A\) ],

\(b=\) [ ][ \(+\) | \(-\) | \(\cdot\) | \(\div\) ] \(\sin\) [ ] \(\degree\) [ \(+\) | \(-\) | \(\cdot\) | \(\div\) ] \(\sin\) [ ] \(\degree\) ,

\(b=\) [ ] \(\sin\) [ ] \(\degree\) ,

\(b\) [ \(≠\) | \(=\) | \(≈\) ][ ].

3. По теореме синусов \(\dfrac{a}{\sin A}=\dfrac{c}{\sin C}\) , тогда:

\(c=(a\) [ \(+\) | \(-\) | \(\cdot\) | \(\div\) ][ \(\sin A\) | \(\sin C\) ] \()\) [ \(+\) | \(-\) | \(\cdot\) | \(\div\) ][ \(\sin C\) | \(\sin A\) ],

\(c=\) [ ][ \(+\) | \(-\) | \(\cdot\) | \(\div\) ] \(\sin\) [ ] \(\degree\) [ \(+\) | \(-\) | \(\cdot\) | \(\div\) ] \(\sin\) [ ] \(\degree\) ,

\(c=\) [ ] \(\sin\) [ ] \(\degree\) ,

\(c\) [ \(≠\) | \(=\) | \(≈\) ][ ].

Ответ: \(∠A=\) [ ] \(\degree\) , \(b\) [ \(≠\) | \(=\) | \(≈\) ][ ], \(c\) [ \(≠\) | \(=\) | \(≈\) ][ ].