Download 10.5 Trigonometry and Area - Cardinal O'Hara High School

10.5 Trigonometry and Area
• What is the area of a regular nonagon with 10-cm
sides?
360
mPCR 
 40
9
1
mPCS  (40)  20
2
5
tan 20 
a
5
a
tan 20
1
A  ap
2
1
5
2
A 
 90  618cm.
2 tan 20
Finding Area
• A stop sign is a regular octagon. The standard size
has a 16.2-in. radius. What is the area of the stop
sign to the nearest square inch?
360
 45
8
mC  22.5
a
cos 22.5 
16.2
16.2(cos 22.5 )  a
x
sin 22.5 
16.2
16(sin 22.5 )  x
p  8  2x
 742.2924146
p  8  2 16.2(sin 22.5 )
 742in.
2
 259.2(sin 22.5 )
1
A  ap
2
1
 16.2(cos 22.5)  259.2(sin 22.5)
2
Area of a Triangle Given SAS
• The area of a triangle is half the product of the
lengths of two sides and the sine of the
included angle.
1
Areaof ABC  bc(sin A)
2
Finding Area
• What is the area of the triangle?
1
A  12  21 sin 48
2
 93.63624801
 94cm.
2
More Practice!!!!!
• Homework – Textbook p. 646 #6 – 18 EVEN.