Answer:
First option: cos(θ + φ) = -117/125
Step-by-step explanation:
Recall that cos(θ + φ) = cos(θ)cos(φ) - sin(θ)sin(φ)
If sin(θ) = -3/5 in Quadrant III, then cos(θ) = -4/5.
Since tan(φ) = sin(φ)/cos(φ), then sin(φ) = -7/25 and cos(φ) = 24/25 in Quadrant II.
Therefore:
cos(θ + φ) = cos(θ)cos(φ) - sin(θ)sin(φ)
cos(θ + φ) = (-4/5)(24/25) - (-3/5)(-7/25)
cos(θ + φ) = (-96/125) - (21/125)
cos(θ + φ) = -96/125 - 21/125
cos(θ + φ) = -117/125
The correct answer to your question is "A".
The answer is 115 because the interior angle is 65 and 115 plus 65 is 180. You want 180 because the angles are opposite and make a straight line
Answer:
A
Step-by-step explanation:
First, we need to find the unknown angle of the triangle.
40 + 20 = 60
180 - 60 = 120
So the unknown angle is 120.
Then, we can use the law of sines to create a proportion.
sin(120)/8 = sin(40)/a
Then, we can simplify this.
a is about 5.9, or answer choice A.
Divide 42 by 4 for one fourth. Divide 13.5 by 5 and multiply that by 2.
