Answer: 6.82
Step-by-step explanation:
So we know the Law of Sines which is that Sin A/a = Sin B/b = Sin C/c. The Sin on top of the fraction is the angle, and the letter on the bottom is the side opposite from that angle.
Our first step is going to be finding the last angle. We have 2 angles already, but one that's missing. We know that all triangles' angles add up to 180, so we can add 68+40=108. Then do 180-108 to get 72. Now we know the third and final angle.
Ok so back to Law of Sines. Now we can plug into that equation. We only need Sin A/a = Sin B/b (It doesn't matter what order you put them in). And remember the lowercase letter at the bottom represents the OPPOSITE side from one of the angles. Since the problem wants the side opposite Sin 68, let's set up a proportion.
Set up we have what we know. We know one side, and opposite that is the angle we already solved for. Now we can cross multiply and end up with:
Since we want to isolate x, we can divide each side by Sin 72.
x= 7(Sin 68)/Sin 72
So now let's put it into the calculator:
7(Sin 68)=6.2853
Now let's divide 6.2853/Sin 72
And you should be left with 6.82 if you round it!
Answer:
lcm for cuberoot
2*2*2*5*5*5*3*3*3
for cuberoot we will make pairs of common three numbers and write them one time
2*5*3
30
check 30*30*30=27000
cube
multiply 27000 three times with itself
19683000000000.0 is the answer
Answer:
- arc second of longitude: 75.322 ft
- arc second of latitude: 101.355 ft
Explanation:
The circumference of the earth at the given radius is ...
2π(20,906,000 ft) ≈ 131,356,272 ft
If that circumference represents 360°, as it does for latitude, then we can find the length of an arc-second by dividing by the number of arc-seconds in 360°. That number is ...
(360°/circle)×(60 min/°)×(60 sec/min) = 1,296,000 sec/circle
Then one arc-second is
(131,356,272 ft/circle)/(1,296,000 sec/circle) = 101.355 ft/arc-second
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Each degree of latitude has the same spacing as every other degree of latitude everywhere. So, this distance is the length of one arc-second of latitude: 101.355 ft.
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<em>Comment on these distance measures</em>
We consider the Earth to have a spherical shape for this problem. It is worth noting that the measure of one degree of latitude is almost exactly 1 nautical mile--an easy relationship to remember.
Answer:
sinθ = -0.554
tanθ = -0.667
secθ = 1.203
Step-by-step explanation:
Consider the point (3, -2)
The value of x is positive and the value of y is negative.
It means the the terminal sides of angle lies in 4rth quadrant, such that:
Base = 3
Perpendicular = 2
Hypotenuse² = 2² + 3²
Hypotenuse = 3.61
sinθ = Perpendicular /Hypotenuse
sinθ = 2/3.61
As sine is negative in 4rth quadrant
sinθ = - (2/3.61)
sinθ = -0.554
tanθ = Perpendicular/ Base
tanθ = 2/3
tanθ = 0.667
As tan is negative in 4rth quadrant
tanθ = -0.667
secθ = Hypotenuse/Base
secθ = 3.61/3
secθ = 1.203
secant is positive in 4rth quadrant
