Mathematics: In ΔABC, m B = 22°, m C = 52° and a = 30. Find the length of b to the nearest tenth.

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In ΔABC, m B = 22°, m C = 52° and a = 30. Find the - id22523013930392, meganwintergirl

Ответ:

laykaleb086

12.08.2021

Mathematics

The length of is approximately 11.7.

Step-by-step explanation:

The sum of internal angles in triangles equals 180°, as we know the measures of angles B and C, we determine the measure of angle A by algebraic means:

$A = 180^{\circ}-B-C$ (1)

( $B = 22^{\circ}$ , $C = 52^{\circ}$ )

$A = 180^{\circ}-22^{\circ}-52^{\circ}$

$A = 106^{\circ}$

The length of is found by the Law of Sine:

$\frac{b}{\sin B} = \frac{a}{\sin A}$

$b = a\cdot \left(\frac{\sin B}{\sin A} \right)$

( a = 30 , $A = 106^{\circ}$ , $B = 22^{\circ}$ )

$b = 30\cdot \left(\frac{\sin 22^{\circ}}{\sin 106^{\circ}} \right)$

$b \approx 11.7$

The length of is approximately 11.7.

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In ΔABC, m < B = 22°, m < C = 52° and a = 30. Find the length of b to the nearest tenth.

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