Equation practice with angle addition
1 answer:
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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.
Answer:
See screenshot below
Step-by-step explanation:
Yes Bus Column:
- We need to find an answer for the "no taxi" section. And we have the total and the "yes taxi" section. So, the "yes taxi" section + the "no taxi" section gives you the total. Another way of saying this is total - "yes taxi" = "no taxi"
- 125 - 30 = 95
No Bus Column:
- We need to find the total of the "yes taxi" section and the "no taxi" section. So, if we add those two sections together, we'll get the total
- 90 + 185 = 275
Total column:
- So, this column is really simple to fill out. All we're doing it adding our answers above to get one answer in each section.
- "Yes Taxi" section: 30 + 90 = 120
- "No Taxi" section: 280
- Total section: 125 + 275 = 400
- We could have also done the total section by adding together 120 and 280, but we would get the same answer, anyway.
I hope this helps!
