Answer:
Part 1) The measure of angle A is ![A=80\°](https://tex.z-dn.net/?f=A%3D80%5C%C2%B0)
Part 2) The length side of a is equal to ![a=10.9\ units](https://tex.z-dn.net/?f=a%3D10.9%5C%20units)
Part 3) The length side of b is equal to ![b=6.3\ units](https://tex.z-dn.net/?f=b%3D6.3%5C%20units)
Step-by-step explanation:
step 1
Find the measure of angle A
we know that
The sum of the internal angles of a triangle must be equal to 180 degrees
so
![A+B+C=180\°](https://tex.z-dn.net/?f=A%2BB%2BC%3D180%5C%C2%B0)
substitute the given values
![A+35\°+65\°=180\°](https://tex.z-dn.net/?f=A%2B35%5C%C2%B0%2B65%5C%C2%B0%3D180%5C%C2%B0)
![A+100\°=180\°](https://tex.z-dn.net/?f=A%2B100%5C%C2%B0%3D180%5C%C2%B0)
![A=180\°-100\°=80\°](https://tex.z-dn.net/?f=A%3D180%5C%C2%B0-100%5C%C2%B0%3D80%5C%C2%B0)
step 2
Find the length of side a
Applying the law of sines
![\frac{a}{sin(A)}=\frac{c}{sin(C)}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bsin%28A%29%7D%3D%5Cfrac%7Bc%7D%7Bsin%28C%29%7D)
substitute the given values
![\frac{a}{sin(80\°)}=\frac{10}{sin(65\°)}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%7D%7Bsin%2880%5C%C2%B0%29%7D%3D%5Cfrac%7B10%7D%7Bsin%2865%5C%C2%B0%29%7D)
![a=\frac{10}{sin(65\°)}(sin(80\°))](https://tex.z-dn.net/?f=a%3D%5Cfrac%7B10%7D%7Bsin%2865%5C%C2%B0%29%7D%28sin%2880%5C%C2%B0%29%29)
![a=10.9\ units](https://tex.z-dn.net/?f=a%3D10.9%5C%20units)
step 3
Find the length of side b
Applying the law of sines
![\frac{b}{sin(B)}=\frac{c}{sin(C)}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%7D%7Bsin%28B%29%7D%3D%5Cfrac%7Bc%7D%7Bsin%28C%29%7D)
substitute the given values
![\frac{b}{sin(35\°)}=\frac{10}{sin(65\°)}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%7D%7Bsin%2835%5C%C2%B0%29%7D%3D%5Cfrac%7B10%7D%7Bsin%2865%5C%C2%B0%29%7D)
![b=\frac{10}{sin(65\°)}(sin(35\°))](https://tex.z-dn.net/?f=b%3D%5Cfrac%7B10%7D%7Bsin%2865%5C%C2%B0%29%7D%28sin%2835%5C%C2%B0%29%29)
![b=6.3\ units](https://tex.z-dn.net/?f=b%3D6.3%5C%20units)
Bananas= 2
Apples= 7
Oranges= 11
And in all there are 20 pieces of fruit
Y=10°
If we're solving for the ninety degree angle, which I seem to doubt, then if 3x=90 then 2x=60 giving a missing total of 30. 30/3 equals 10
Answer:
-1.9
Step-by-step explanation:
(a) Yes all six trig functions exist for this point in quadrant III. The only time you'll run into problems is when either x = 0 or y = 0, due to division by zero errors. For instance, if x = 0, then tan(t) = sin(t)/cos(t) will have cos(t) = 0, as x = cos(t). you cannot have zero in the denominator. Since neither coordinate is zero, we don't have such problems.
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(b) The following functions are positive in quadrant III:
tangent, cotangent
The following functions are negative in quadrant III
cosine, sine, secant, cosecant
A short explanation is that x = cos(t) and y = sin(t). The x and y coordinates are negative in quadrant III, so both sine and cosine are negative. Their reciprocal functions secant and cosecant are negative here as well. Combining sine and cosine to get tan = sin/cos, we see that the negatives cancel which is why tangent is positive here. Cotangent is also positive for similar reasons.