How do find you equivelant expressions?
1 answer:
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Answer:
The distance traveled to return directly to the starting point = 34 miles.
Step-by-step explanation:
Given:
Distance covered in north = 16 miles
Distance covered in east = 30 miles
We have to find the displacement (the shortest distance).
Or
Distance traveled to return directly back to the starting point.
Let the origin be O and the distance covered in north be ON and distance covered from right to the east is NE.
Move rightward from N point to the right that is towards east direction.
N is a northern point and E is the eastern point.
ON = miles
NE = miles
We can imagine that it forms a right angled triangle making 90 (deg) at N by joining E with O ,where OE is the
hypotenuse.
Applying Pythagoras formula.
Where,
Hypotenuse =
The distance traveled in returning back to the starting point is equivalent to the measure of the hypotenuse.
So,
Hypotenuse =
=
=
= miles
So the distance traveled to return directly to the starting point = 34 miles.
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!