Answer:
- Exact Area = 210.25pi - 210
- Approximate Area = 450.185
The units for the area are in square inches or in^2. The approximate value shown above is when using pi = 3.14
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Explanation:
Use the pythagorean theorem to find the length of the hypotenuse
a^2 + b^2 = c^2
20^2 + 21^2 = c^2
400 + 441 = c^2
c^2 = 841
c = sqrt(841)
c = 29
The hypotenuse is 29 inches long. This is the diameter of the circle. Half of that is the radius at r = d/2 = 29/2 = 14.5 inches.
The area of the circle is...
A = pi*r^2
A = pi*(14.5)^2
A = pi*210.25
A = 210.25pi
Which is exact in terms of pi
We'll subtract off the triangular region as this isn't shaded in. The area of the triangle is base*height/2 = 20*21/2 = 420/2 = 210 square inches.
So the shaded region is therefore 210.25pi - 210 square inches
This approximates to 210.25*3.14 - 210 = 450.185 when using the approximation pi = 3.14; use more decimal digits of pi to get a more accurate value.
Answer:
116 degrees
Step-by-step explanation:
Supplementary Angles=180 degrees
64+x=180
180-64=116
116=116
Answer:
x = 30°.
Step-by-step explanation:
To calculate the value of 'x', we can first derive the value of one of the angles that make up the triangle.
Notice that there is an angle with a measure of 100°. The angle that makes up the angle of the triangle is called a Vertical Angle. Therefore, if the angle in red is 100°, the vertical angle, or the third angle of the triangle, is 100°.
There are two congruent sides to the triangle, as seen by the congruent lines. This means that both of the other two angles must be equal. Find the value of 'x' by:
180 - 100 = 80. Since the value of one angle was 100°, and the angles in a triangle must add up to 180°, you can simply subtract to find the sum of the other two angles.
(x + 10) + (x + 10) = 80
2x + 20 = 80
2x = 60
x = 30°.
