Approximating Pi

ID: mahas-vabur
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Created by Illustrative MathematicsIllustrative Mathematics, CC BY 4.0
Subject: Geometry
Grade: 9-12
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11 questions

Approximating Pi

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Problem 1

A regular pentagon has side length 7 inches. Round answers to the nearest tenth if necessary.

1) What is the perimeter of the pentagon?

2) What is the area of the pentagon?

Problem 2

The expression nsin(3602n)n \cdot \sin{\left(\frac{360}{2n}\right)} approximates π\pi by giving the perimeter of a regular polygon inscribed in a circle with radius 1.

3) What does nn stand for in the expression?

4) If there are 60 sides, what is the difference between the perimeter and π\pi? Write your answer to five decimal places.

Problem 3

A regular hexagon has side length 2 inches. Round answers to the nearest tenth if necessary.

5) What is the perimeter of the hexagon?

6) What is the area of the hexagon?

Problem 4

An airplane travels 125 miles horizontally during a decrease of 9 miles vertically. Round angles to the nearest whole degree and distances to the nearest tenth of a unit.

7) What is the angle of descent?

8) What is the distance of the plane’s path?

Problem 5

9) Select all\textbf{all} true statements. Write each corresponding letter in the answer box and separate letters with commas.

a) ACAC is 119\sqrt{119} units \quad\quad b) ACAC is 13 units \quad\quad c) cos(θ)=512\cos{(\theta)} = \frac{5}{12} \quad\quad d) sin(α)=1213\sin{(\alpha)} = \frac{12}{13} \quad\quad e) θ=arctan(512)\theta = \arctan{\left(\frac{5}{12}\right)}

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Problem 6

Given triangle ABCABC.

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10) Select all\textbf{all} true statements. Write each corresponding letter in the answer box and separate letters with commas.

a) sin(66°)=x7\sin{(66\degree)} = \frac{x}{7} \quad\quad b) sin(24°)=y7\sin{(24\degree)} = \frac{y}{7} \quad\quad c) cos(66°)=x7\cos{(66\degree)} = \frac{x}{7} \quad\quad d) cos(24°)=x7\cos{(24\degree)} = \frac{x}{7} \quad\quad e) cos(66°)=7y\cos{(66\degree)} = \frac{7}{y}

Problem 7

11) An equilateral triangle has area of 36336\sqrt{3} square units. What is the side length?