2 years ago

CAN SOMEONE HELP PLEASE!!

Mathematics

1 answer:

Illusion [34]2 years ago

3 0

1. Distributive Property.
2.Congruence Property.
3.Subtraction Property.
4.Division Property.

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Answer:

m∠B = 70.0° (nearest tenth)

Step-by-step explanation:

Sine Rule for Angles

$\sf \dfrac{\sin A}{a}=\dfrac{\sin B}{b}=\dfrac{\sin C}{c}$

(where A, B and C are the angles and a, b and c are the sides opposite the angles)

Given:

a = 13
c = 19
A = 40°

Substituting the given values into the formula to find m∠C:

$\implies \sf \dfrac{\sin 40^{\circ}}{13}=\dfrac{\sin C}{19}$

$\implies \sf \sin C=\dfrac{19\sin 40^{\circ}}{13}$

$\implies \sf C=\sin^{-1}\left(\dfrac{19\sin 40^{\circ}}{13}\right)$

$\implies \sf m \angle C=69.96086904^{\circ}$

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$\implies \sf m \angle A+ m \angle B+m \angle C=180^{\circ}$

$\implies \sf 40^{\circ} + m \angle B+69.960...^{\circ}=180^{\circ}$

$\implies \sf m \angle B=70.03913...^{\circ}$

Therefore, m∠B = 70.0° (nearest tenth)

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