Question

HELP i can’t figure this out

Answer 1

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

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

where A, B and C are the angles and a, b and c are the side lengths opposite the angles.

Therefore,

$\dfrac{a}{sin(23.7)}=\dfrac{b}{sin(66.3)}=\dfrac{0.0793}{sin(90)}$

$\implies a=\dfrac{0.0793}{sin(90)}\times sin(23.7)=0.031874458...=0.0319$

$\implies b=\dfrac{0.0793}{sin(90)} \times sin(66.3)=0.072612043...=0.0726$