Sure, that's what solving triangles is. Trigonometry has a short menu. Basically we choose between three formulas: Law of Sines, Law of Cosines, Sum of Triangle Angles
The Law of Sines has two sides and two opposite angles; given any three we can solve for the fourth.
The Law of Cosines has three sides and one angle; again given any three we solve for the remaining one.
The Sum of Triangle Angles says all three angles add to 180 degrees, so given two we can find the third.
Here we have all the angles and one side, that's Law of Sines to get the remaining sides.
2. marking choreography is essential to your memory of the dance without having to go all out of each time to practice.
Answer: 9 / 11
That is approximately 0.82
Explanation:
The ratio of two quantities x and y is x divided by y, i.e. the quotient x / y.
So, the ratio of Sylia's work time to Paul's work time is:
Sylvia's work time
---------------------------
Paul's work time
Given that you have the times in mixed units, hours and minutes, you must convert to one of the, either hours or minutes.
If you choose to work with hours, this is the work:
1) Silvia's time: 3 hours and 45 minutes = 3 hours + 45 / 60 hours = 3hours + 0.75 hours = 3.75 hours
2) Paul's work time: 4 hours and 35 minutes = 4 hours + 35/60 hours = 4 hours + 7/12 hours = (48+7)/12 = 55/12 hours ≈ 4.58 hours
3) Ratio:
Sylvia's work time 3.75 hours 3.75*12 45 9
------------------------- = --------------------- = ---------------- = -------- = -----
Paul's work time (55/12) hours 55 55 11
≈ 0.82
You can calculate the ratio using minutes and shall obtain the same result. Look:
1) 3 hours + 45 minutes = 3 * 60 minutes + 45 minutes = 180 minutes + 45 minutes = 225 minutes
2) 4 hours + 35 minutes = 4*60 minutes + 35 minutes = 240 minutes + 35 minutes = 275 minutes
3)
225 minutes 9
----------------- = ------, which is the same result obtained above.
275 minutes 11
Since the two lines are parallel then they have the same slope which = 1/3
since the line passes through (-6 , -8)
y+8 = (1/3)(x+6)
3y + 24 = x + 6
x - 3y = 18 is the equation
4 1/2 = 9/2
5/9 x 9/2 = 45/18
