If the value of cos(θ) is negative, this angle (θ) can only be in one of two quadrants; the sine quadrant or the tan quadrant. In the sine quadrant, tan(θ) must be negative, but since tan(θ) > 0, we can safely say that the angle (<span>θ) is based in the tan quadrant.
We know that cos(</span><span>θ) = - Adjacent / Hypotenuse, and in this case Adjacent = 2 and Hypotenuse = 5. Using Pythagoras' theorem, we can find the opposite side of the right angled triangle situated in the tan quadrant...
</span>Adjacent² + Opposite² = Hypotenuse²
Therefore:
2² + Opposite² = 5²
Opposite² = 5² - 2²
Opposite² = 21
Opposite = √(21)
------------
Now, sin(θ) must be negative, as the right angled triangle is in the tan quadrant. We also know that sin(<span>θ) = Opposite / Hypotenuse, therefore:
sin(</span><span>θ) = - [</span>√(21)]/[5]
Answer:
$6.96
Step-by-step explanation:
(4*8.99) + (3*7)
35.96 + 21 = 56.96
50- 56.96 = -6.96 So she owes 6.96
Answer:
x=32, y=36, and z=25
Step-by-step explanation:
There are only two sums the equations can all add up to, 67 degrees and 113 degrees. I know that to the equation with x is equal to 67 degrees.
2x+3=67
2x=64 (subtract 3)
x=32 (divide by 2)
Now to find the measurement of the other angle, we subtract 180 and 67 since the measurement of a line is 180 degrees.
180-67=113
The equations of y and z are both equal to 113.
3y+5=113 4z+13=113
3y=108 (subtract 5) 4z=100 (subtract 13)
y=36 (divide by 3) z=25 (divide by 4)
Answer:
i want ponts
Step-by-step explanation:
Answer:
The number of times Abigail is faster on her skateboard than she is walking is 2 times faster
Step-by-step explanation:
Let the distance to Abigail's home = D
The distance Abigail had traveled before hr skateboard broke = 2/3·D
The distance from home where the skateboard broke = D - 2/3·D = 1/3·D
The time it took Abigail to walk the 1/3·D home = Twice the time it will take her if she was on her skateboard
Let the time it will take Abigail to travel the 1/3·D home on her skateboard = t
Therefore;
The time it took Abigail to walk the 1/3·D home = 2 × t
The speed of Abigail walking, = Distance/Time = 1/3·D/(2 × t) = D/(2·t)
The speed of Abigail skateboarding, = Distance/Time =D/t
The ratio of the speed of Abigail skateboarding to the speed of Abigail walking =
Therefore, Abigail is two times faster on her skateboard than she is walking.