3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679
Answer:
C. 54π + 20.25√3 cm²
Step-by-step explanation:
The shaded area can be split into two areas: a sector and an isosceles triangle.
Area of a sector is:
A = (θ/360°) πr²
where θ is the central angle and r is the radius.
Area of an isosceles triangle can be found with SAS formula:
A = ½ ab sin θ
where a and b are two sides of a triangle and θ is the angle between them.
In this case, r = a = b = 9 cm. The central angle of the sector is 240°, and the vertex angle of the triangle is 120°. Therefore, the total area is:
A = (240°/360°) π (9 cm)² + ½ (9 cm) (9 cm) sin 120°
A = 54π + 20.25√3 cm²
Applying the definition of alternate angles and angles on a straight-line: <u>m<ACB = 84°.</u>
<em><u>Recall:</u></em>
- Alternate angles are congruent and have equal angle measures.
- Angles on a straight-line = 180 degrees.
<em>The diagram showing the information and sketch of the Highland Park is attached below (see attachment).</em>
<em />
<em><u>Thus:</u></em>
m<BAC = 36° (given)
m<BCE = 60° (given)
<ACD = <BAC (alternate angles)
m<ACD = 36°
m<ACB = 180° - (m<ACD + m<BCE) (angles on a straight-line)
m<ACB = 180° - (36° + 60°)
m<ACB = 84°
Thus, applying the definition of alternate angles and angles on a straight-line: <u>m<ACB = 84°.</u>
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brainly.com/question/15234579