Polygons, Pythagoras & Trig Ratios

POLYGONS

100

Work out the sum of the INTERIOR angles for a polygon with:

a. 20 sides

b. 45 sides

a. (20 – 2) × 180 = 3240°

b. (45 – 2) × 180 = 7740°

200

Work out the number of sides of a polygon with the sum of the INTERIOR angles:

a.  2880°

b.  1980°

a.  2880 = (n - 2) x 180

     n = 18 sides

b.  1980 = (n - 2) x 180

     n = 13 sides

300

Calculate the number of sides of a regular polygon with an exterior angle of:

a.  36°

b.  24°

a. 360 ÷ 36 = 10 sides

b. 360 ÷ 24 = 15 sides

400

A regular polygon has an interior angle that is five times larger than its exterior angle. 

How many sides does the regular polygon have?

x + 5x = 180°

6x       = 180°

x         = 30°

360° / 30° = 12 sides

500

x = 126°

Pythagoras

100

Find the value of C. 

Give the answer correct to 2 decimal places

c² = 4² + 6²

c = √(16 + 36)

   = 7.21

200

Find the value of x. 

Give the answer correct to 2 decimal places.

20² = 14² + x²

x²  = 20² - 14² 

x = √(400 - 196)

   = 14.28

300

Find the value of x and y.

5² = 3² + x²

x = √(25 - 9)

   = 4

6² = 4² + y²

x = √(36 - 16)

   = 4.47

400

Find the value of x

h² = 20² + 15²

h = √(400 + 225)

   = 25 cm

x² = 25² + 18.75²

x   = √ (625 + 351.5625)

     = 31.25 cm

Trig ratios

100

Name the sides AB, BC and AC

AB -> Adjacent

BC -> Opposite

AC -> Hypotenuse

200

Find the value of x. 

Give your answer correct to 2 significant figure

Cos 55° = 23 / x

x = 23 / Cos 55°

   = 40 cm

300

Find the length of the side O. 

Give your answer correct to 2 significant figures

Tan 71° = O / 6

O = 6 Tan 71°

   = 17 cm

400

Find the value of x. 

Give your answer correct to whole number

Tan 35° = 115  /  base_B

base_B = 115  / Tan 35°

        = 164 cm

Tan 56° = 115  /  base_S

base_S = 115  / Tan 56°

        = 78 cm

x = 164 - 78

   = 86 cm