Lesson 11

Approximating Pi

  • Let’s approximate the value of pi.

Problem 1

Technology required. A regular pentagon has side length 7 inches. 

  1. What is the perimeter of the pentagon? 
  2. What is the area of the pentagon? 

Problem 2

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

  1. What does \(n\) stand for in the expression? 
  2. If there are 60 sides, what is the difference between the perimeter and \(\pi\)? 

Problem 3

Technology required. A regular hexagon has side length 2 inches. 

  1. What is the perimeter of the hexagon? 
  2. What is the area of the hexagon? 
(From Unit 4, Lesson 10.)

Problem 4

An airplane travels 125 miles horizontally during a decrease of 9 miles vertically.

  1. What is the angle of descent?
  2. What is the distance of the plane’s path?
(From Unit 4, Lesson 10.)

Problem 5

Select all true statements.

Right triangle A B C. Side A B is 5 units, B C is 12. Angle B A C labeled alpha, angle A C B labeled theta.
A:

\(AC\) is \(\sqrt{119}\) units

B:

\(AC\) is 13 units

C:

\(\cos(\theta) = \frac {5}{12}\)

D:

\(\sin(\alpha) = \frac{12}{13}\)

E:

\(\theta=\arctan \left(\frac{5}{12}\right)\)

(From Unit 4, Lesson 9.)

Problem 6

Write 2 equations using sine and 2 equations using cosine based on triangle \(ABC\). 

Right triangle ABC. Angle C = 90 degrees. Angle B = 66 degrees. Angle A = 24 degrees. AB = 7. BC = y. AC = x.
(From Unit 4, Lesson 8.)

Problem 7

An equilateral triangle has area of \(36 \sqrt3\) square units. What is the side length? 

(From Unit 4, Lesson 3.)