Respuesta :
Answer:
As Per Provided Information
Radius of sector 5 units
Area of sector 18.751 square units
we have been asked to determine the measure of the central angle .
Using Formulae
[tex]\underline{ \boxed{\bf\pink{Area_{(Sector)} \: = \cfrac{ \theta \times \pi {r}^{2} }{360 {}^{ \circ}}}}}[/tex]
Substituting the given value and let's solve it
[tex] \longrightarrow \sf \: 18.751 = \cfrac{ \theta \times 3.14 \times {5}^{2} }{360} \\ \\ \ \\ \longrightarrow \sf \: 18.751 \times 360 = { \theta \times 3.14 \times 25} \\ \\ \\ \longrightarrow \sf \: 6750.36 \: = \theta \: \times 78.5 \\ \\ \\ \longrightarrow \sf \theta \: = \: \cfrac{6750.36}{78.5} \\ \\ \\ \longrightarrow \sf \theta \: = \cancel\cfrac{6750.36}{78.5} \\ \\ \\ \longrightarrow \sf \theta \: = 85.99 {}^{ \circ} \\ \\ \\ \longrightarrow \sf \theta \: = \: \approx \: 86 {}^{ \circ} [/tex]
Therefore,
- Measure of central angle is 86°
