Answer:
The area of triangle is ![A=58.02\ ft^{2}](https://tex.z-dn.net/?f=A%3D58.02%5C%20ft%5E%7B2%7D)
Step-by-step explanation:
Let
B -----> the measure of the vertex angle of the isosceles triangle ABC
a and c -----> the two congruent sides of the isosceles triangle ABC
we know that
The area of a triangle applying the law of sines is equal to
![A=\frac{1}{2}(a)(c)sin(B)](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%28a%29%28c%29sin%28B%29)
we have
![a=c=17.91\ ft](https://tex.z-dn.net/?f=a%3Dc%3D17.91%5C%20ft)
![B=21.21\°](https://tex.z-dn.net/?f=B%3D21.21%5C%C2%B0)
substitute in the formula
![A=\frac{1}{2}(17.91)(17.91)sin(21.21\°)](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%2817.91%29%2817.91%29sin%2821.21%5C%C2%B0%29)
![A=58.02\ ft^{2}](https://tex.z-dn.net/?f=A%3D58.02%5C%20ft%5E%7B2%7D)
The common denominator is 40.
Answer:
radians
Step-by-step explanation:
Arc length and radius is given. So, we need to know the arc length formula for a circle.
That is:
![s=r\theta](https://tex.z-dn.net/?f=s%3Dr%5Ctheta)
Where s is the arc length
r is the radius
is the angle (IN RADIANS)
We have:
s = 15.5
r = 9
Now, we substitute and find the angle:
![s=r\theta\\15.5=9\theta\\\theta=\frac{15.5}{9}\\\theta=1.72](https://tex.z-dn.net/?f=s%3Dr%5Ctheta%5C%5C15.5%3D9%5Ctheta%5C%5C%5Ctheta%3D%5Cfrac%7B15.5%7D%7B9%7D%5C%5C%5Ctheta%3D1.72)
The angle, in radians, in 1.72
I'm assuming the pail holds 6 3/4 (not 634) gallons of water.
1 gallon= 16 cups
Multiply total gallons by cups per 1 gallon.
= 6 3/4 cups * 16 cups/gallon
convert mixed number to improper fraction
= 27/4 * 16
multiply numerators
= (27*16)/4
multiply in parentheses
= 432/4
= 108 cups
ANSWER: There are 108 cups
Hope this helps! :)