What is the area of a regular nonagon with 10 cm sides and an apothem if 6cm?
1 answer:
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Answer:
m∠QPM=43°
Step-by-step explanation:
see the attached figure to better understand the problem
we know that
m∠NPQ=m∠MPN+m∠MPQ
we have
m∠NPQ=(9x-25)°
m∠MPN=(4x+12)°
m∠MPQ=(3x-5)°
substitute the given values and solve for x
(9x-25)°=(4x+12)°+(3x-5)°
(9x-25)°=(7x+7)°
9x-7x=25+7
2x=32
x=16
Find the measure of angle QPM
Remember that
m∠QPM=m∠MPQ
m∠MPQ=(3x-5)°
substitute the value of x
m∠MPQ=(3(16)-5)=43°
therefore
m∠QPM=43°
Answer:
the Pythagorean theorem states: a^2 + b^2 = c^2
1) in this case a=18 and b1=25
18^2 + 25^2 = c1^2
324 + 625 = c1^2
949 = c1^2
√949 = c1
cca. 30.8 = c1
2) in this case a=18 and b' = b2 - b1 = 40 - 25 = 15
in the picture im attaching i highlighted the triangles we are working with, and there you can clearly see that b' (the horizontal line at the bottom of the red tr.) is the difference between the lines b2 and b1
now you can use the same technique as in the first case, and the final answer will be cca. 23.4 = c2
3) in this case a=18 and b'' = b4 - b3 = 75 - 55 = 20
same thing as number 2, final answer cca. 26.9 = c3
