Lesson 11

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? 

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 \(\pi\)? 

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? 

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?

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

\(AC\) is 13 units

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

\(\sin(\alpha) = \frac{12}{13}\)

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

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

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