# Approximating Pi

11 questions

# Approximating Pi

##### 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?