Approximating Pi

ID: mahas-vabur
Illustrative Mathematics, CC BY 4.0
Subject: Geometry

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

3) What does ﻿$n$﻿ stand for in the expression?

4) If there are 60 sides, what is the difference between the perimeter and ﻿$\pi$﻿? 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 ﻿$\textbf{all}$﻿ true statements. Write each corresponding letter in the answer box and separate letters with commas.

a) ﻿$AC$﻿ is ﻿$\sqrt{119}$﻿ units ﻿$\quad\quad$﻿ b) ﻿$AC$﻿ is 13 units ﻿$\quad\quad$﻿ c) ﻿$\cos{(\theta)} = \frac{5}{12}$﻿ ﻿$\quad\quad$﻿ d) ﻿$\sin{(\alpha)} = \frac{12}{13}$﻿ ﻿$\quad\quad$﻿ e) ﻿$\theta = \arctan{\left(\frac{5}{12}\right)}$﻿

Problem 6

Given triangle ﻿$ABC$﻿.

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

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

Problem 7

11) An equilateral triangle has area of ﻿$36\sqrt{3}$﻿ square units. What is the side length?