For a problem of this nature, we need to assume that the base of the observation tower is at the same elevation as the fire. The tangent of the angle is the ratio of tower height to horizontal distance:
tan(α) = (tower height)/(horizontal distance)
Rearranging this equation, we have
(horizontal distance) = (tower height)/tan(α)
Putting in the given values gives
(horizontal distance) = (90 ft)/tan(7°) ≈ 733 ft
Oh boy. I don't know how to solve this off the top of my head so this answer may ramble a bit as I figure it out as I go along.
At least two numbers have to be close in value, one positive and one negative, in order for a+b+c to be true
Let's see, ABC=-12
If one letter was 4, 1, and -3 they would add to 2 and multiply to -12. I got these by just trying a bunch of combinations.
I'm pretty sure these are the right numbers, but which is which we need the AB+BC+AC formula to figure out.
IF: a=4 b=1 c=-3
4 -3 -12 = -11. Wow, first try, for reals!
A equals 4. B=1. C=-3
Would other combinations work?
a=1 b=-3 c=4
-3 + -12 + 4 = -11
Yes, other combinations work as well. Well, you have your numbers and two ways they can go. Hope this helps!
The number of people is:
1+5= 6
$75/ 6 people= $12.50/ person.
Each person pays $12.50~
Answer: B) Right angles are congruent
This is another way of saying "all 90 degrees are the same measure". The square angle marker indicates a right or 90 degree angle.
<u>Given</u>:
The circumference of the smaller is 30% of the circumference of the larger circle.
We need to determine the circumference of the larger circle.
<u>Diameter of the larger circle:</u>
The diameter of the smaller circle is 9 in.
Since, the circumference of the smaller is 30% of the circumference of the larger circle, we have;
![S=0.3L](https://tex.z-dn.net/?f=S%3D0.3L)
where S is the circumference of the smaller circle and L is the circumference of the larger circule.
![\pi(9)=(0.3)\pi d](https://tex.z-dn.net/?f=%5Cpi%289%29%3D%280.3%29%5Cpi%20d)
![9=0.3d](https://tex.z-dn.net/?f=9%3D0.3d)
![30=d](https://tex.z-dn.net/?f=30%3Dd)
Thus, the diameter of the larger circle is 30 inches.
<u>Circumference of the larger circle:</u>
The circumference of the larger circle is given by
![C=\pi d](https://tex.z-dn.net/?f=C%3D%5Cpi%20d)
![C=3.14\times 30](https://tex.z-dn.net/?f=C%3D3.14%5Ctimes%2030)
![C=94.2](https://tex.z-dn.net/?f=C%3D94.2)
Thus, the circumference of the larger circle is 94.2 inches.