# Lesson 11

Approximating Pi

### Problem 1

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

- What is the perimeter of the pentagon?
- What is the area of the pentagon?

### Solution

For access, consult one of our IM Certified Partners.

### 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.

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

### Solution

For access, consult one of our IM Certified Partners.

### Problem 3

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

- What is the perimeter of the hexagon?
- What is the area of the hexagon?

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 4, Lesson 10.)### Problem 4

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

- What is the angle of descent?
- What is the distance of the plane’s path?

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 4, Lesson 10.)### Problem 5

Select **all** true statements.

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

\(AC\) is 13 units

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

\(\sin(\alpha) = \frac{12}{13}\)

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

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 4, Lesson 9.)### Problem 6

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

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 4, Lesson 8.)### Problem 7

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

### Solution

For access, consult one of our IM Certified Partners.

(From Unit 4, Lesson 3.)