Deriving trigonometric ratios using regular polygon
Answers
Answer:
It is hard for me to embed an image in the appropriate response, so you should peruse this with a pencil close by.
Sketch a standard 9-gon. Join the focal point of the 9-gon to the 9 vertices. This partitions the 9-gon into 9 consistent triangles. To discover the region of the 9-gon, we will discover the region of one of these triangles, and duplicate the outcome by 9.
Focus now on one of these triangles AOB, where O is the inside and An and B are two successive vertices. We will discover the zone of △AOB.
We have AB=8 and ∠AOB=360∘9=40∘.
Drop an opposite from O to AB, meeting AB at M. Note that ∠AOM=20∘.
Additionally, AMOM=tan(20∘). Be that as it may, AM=4, so OM=4tan(20∘).
Presently we know the base AB of △AOB and the tallness OM. The zone of △AOM is along these lines 12⋅8⋅4tan(20∘).
At long last, duplicate by 9 and disentangle a bit. We get 144tan(20∘), or in the event that you like, 144tan(70∘
Answer:
(n-2) × 180° / n
Step-by-step explanation:
Any n-sided regular polygon can be divided into (n-2) triangles
Sum of angles of a triangle = 180°
Sum of (n-2) Triangles =(n-2) × 180°
All angles in regular polygon are equals
Measure of one angle of regular polygon = (n-2) × 180° / n