A square is inscribed in a circle. How much larger is the area of the circle than the area of the square?
1 answer:
Answer:
π/2 : 1 or π : 2
Step-by-step explanation:
In the attachments I have a picture of a square inscribed in a circle.
Call the side of the square a. Therefore, the area of the square is a^2.
We can also see that the diagonal of the square is the circle's diameter.
Using the Pythagorean Theorem we find that the diagonal/diameter of the circle is a√2. Thus the radius is that divided by 2, which is (a√2)/2.
We also know that the formula for a circle's area is πr^2, so the area of the circle is π((a√2)/2)^2 --> π(a^2)(2)/4 --> π(a^2)/2.
Hence the ratio of the circle to the square is π(a^2)/2 to a^2 which is π/2 to 1 or π to 2.
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<u>Answer:</u>
A building makes a angle with the ground .The two interior angles are
and
<u>Solution: </u>
Given, a ladder which is against the building wall makes an exterior angle of
And building makes a angle with the ground.
So, altogether it makes a right angle triangle with ladder as hypotenuse and ground as base leg and building as another leg.
Now, we know that, sum of exterior angles and interior angles equals to
Here, in the case of ground and ladder, exterior angle is and interior angle is unknown.
Exterior angle + interior angle = 180
110 + interior angle = 180
Interior angle = 180 – 110
Interior angle =
We have found one of the two interior angles of right angle triangle.
We know that, sum of angles in a triangle is 180 degree
Known Interior angle + unknown interior angle + right angle = 180
70 + unknown interior angle + 90 = 180
Unknown interior angle + 160 = 180
Unknown interior angle = 180 - 160
Unknown interior angle =
Hence the two interior angles are and