Looking for the area of a regular figure would be taking the longest side and the shortest side and multiply
Answer:
22
Step-by-step explanation:
After spending 3/7, she is left with;
4/7
Now, 4/7 is equivalent to 72
7/7 is equivalent to?
= 126 dollars
Answer:
radius = 13
Step-by-step explanation:
Look at the attached picture below. We can calculate radius with the help of the Pythagorean theorem. But first we have to find out the values of the two legs.
First let's find the shorter leg.
<u>Equidistant Chords Theorem</u>
Two chords are congruent if they are equidistant from the center.
Chords in the picture are congruent and that means that the distance from the center to each of them is the same!
Let's calculate the distance. But to get the distance we have to find x first.
Since the distances are the same:
Therefore:
Let's focus on the longer leg. Since part of the radius is perpendicular to the chord, it actually bisects the chord! That means that the long leg is going to be a half of the length of the chord.
Therefore:
All that is left is the Pythagorean Theorem in the right triangle.
<u>Pythagorean Theorem</u>
Hypotenuse in our case is the radius.
For , on the left we have , and on the right,
(where we use the double angle identity: )
Suppose the relation holds for :
Then for , the left side is
So we want to show that
On the left side, we can combine the fractions:
Recall that
so that we can write
(another double angle identity: )
Then recall that
which lets us consolidate the numerator to get what we wanted:
and the identity is established.