# Lesson 11

Approximating 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?

### Solution

(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?

### Solution

(From Unit 4, Lesson 10.)

### Problem 5

Select all true statements.

A:

$$AC$$ is $$\sqrt{119}$$ units

B:

$$AC$$ is 13 units

C:

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

D:

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

E:

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

### Solution

(From Unit 4, Lesson 9.)

### Problem 6

Write 2 equations using sine and 2 equations using cosine based on triangle $$ABC$$

### Solution

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