SOLUTION: Three Questions: 1. Find the area of the segment of a circle whose radius is 10inches, formed by a central angle of 80 degrees. 2. The sides of a parallelogram are 4 cm and 6

Question 37635This question is from textbook
: Three Questions:
1. Find the area of the segment of a circle whose radius is 10inches, formed by a central angle of 80 degrees.
2. The sides of a parallelogram are 4 cm and 6 cm. One angle is 55 degrees. Find the lengths of the diagonal of the parallelogram.
3. Two factories blow their whistles at exactly 5:00 pm/ A man hears the two blasts at 3 seconds and 6 seconds after 5:00, respectively. The angle between his lines of sight to the factories is 42.2 degrees. If sound travels 344 meters per second, how far apart are the factories? This question is from textbook

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1. Find the area of the segment of a circle whose radius is 10inches, formed by a central angle of 80 degrees.
Area of circle = (pi)10^2 = 100pi sq in
Area of segment = (80/360)100pi= (2/9)100pi=69.81..sq. in.
2. The sides of a parallelogram are 4 cm and 6 cm. One angle is 55 degrees. Find the lengths of the diagonal of the parallelogram.
Draw the picture. Use the Law of Cosines to get:
diagonal^2 = 4^2+6^2-2(4)(6)Cos(55 degrees)
Then take the square root to get diagonal.

3. Two factories blow their whistles at exactly 5:00 pm/ A man hears the two blasts at 3 seconds and 6 seconds after 5:00, respectively. The angle between his lines of sight to the factories is 42.2 degrees. If sound travels 344 meters per second, how far apart are the factories?
Draw the picture, then use the Law of Cosines to get:
distance^2=[3(344)]^2 =[6(344)]^2-2(3(344)(6(344))Cos(42.2 degrees)
Then take the square root to get the distance.
Cheers,
Stan H.

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