3. The area of a circle is [tex] \pi r^{2}
[/tex]
This means that the "r" is the radius and in this case it is 5 in.
[tex] \pi (5)^{2} = 78.54 [/tex]
4. The circumference of a circle is : [tex] 2\pi r [/tex]
This means: [tex] 2\pi (5) = 31.42 [/tex]
5. We know that the two sides are 5 in. and the angle in the center for both triangles is 90 degrees. A triangle is always 180 degrees in total so we can say that the other two angles must add up to 90 degrees and they are equal so; 90/2 = 45 degrees.
This means that the other two angles are 45 degrees each.
We can use some trigonometry to solve for the missing side;
cos(theta) = adjacent/ hypotenuse
hypotenuse = adjacent / (cos(theta)) .... hypotenuse = 5/ (cos(45)) ... hypotenuse = 7.07
Half of that is 3.535
Area of a triangle = bh/2 .... (7.07 * h)/2
sin(45) = opposite /5 .... 5sin(45) = opposite = 3.54
(3.54 * 7.07) / 2 = 12.5
