Answer:
m∠B = 66.3°
a = 0.0319
b = 0.0726
Step-by-step explanation:
Sum of the interior angles of a triangle = 180°
⇒ m∠A + m∠B + m∠C = 180°
⇒ 23.7 + m∠B + 90 = 180
⇒ m∠B = 180 - 90 - 23.7 = 66.3°
We can use the sine rule to help solve the missing side lengths.
Sine rule
[tex]\dfrac{a}{sin(A)}=\dfrac{b}{sin(B)}=\dfrac{c}{sin(C)}[/tex]
where A, B and C are the angles and a, b and c are the side lengths opposite the angles.
Therefore,
[tex]\dfrac{a}{sin(23.7)}=\dfrac{b}{sin(66.3)}=\dfrac{0.0793}{sin(90)}[/tex]
[tex]\implies a=\dfrac{0.0793}{sin(90)}\times sin(23.7)=0.031874458...=0.0319[/tex]
[tex]\implies b=\dfrac{0.0793}{sin(90)} \times sin(66.3)=0.072612043...=0.0726[/tex]
