Question

HELP i can’t figure this out

Answer 1

m∠B = 66.3°

a = 0.0319

b = 0.0726

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

`(a)/(sin(A))=(b)/(sin(B))=(c)/(sin(C))`

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

Therefore,

`(a)/(sin(23.7))=(b)/(sin(66.3))=(0.0793)/(sin(90))`

`\implies a=(0.0793)/(sin(90))* sin(23.7)=0.031874458...=0.0319`

`\implies b=(0.0793)/(sin(90)) * sin(66.3)=0.072612043...=0.0726`