Answer:
There are two ways to do this problem algebraically or trigonometrically.
Algebraically/geometrically
The ratios of the sides of a 30/60/90 tri. are x, x√3, 2x (short leg, long leg, hyp). Therefore, if the long leg is 6 'units'. then 6 = x√3. x = 6√3.
The hyp is 2x then the hypotenuse is 2(6√3) = 12√3, rationalizing is 12√3/3 = 4√3
Using Trig.
We can use sinx = y/r = opp/hyp. The long leg of 6 is opposite 60 degrees (pi/3).
Therefore, sin(pi/3) = 6/r =
r = 6/sin(pi/3) = 6/(√3/2) = 12/√3, when you rationalize you get 12√3/3 = 4√3
9514 1404 393
Answer:
23, 49
Step-by-step explanation:
Let s represent the smaller of the two numbers. Then the larger is s+26, and the sum is ...
s + (s+26) = 72
2s = 72 -26
s = (72 -26)/2 = 23
Then the larger number is
s +26 = 49
The two numbers are 23 and 49.
_____
The reason we wrote the solution this way is to show you that the smaller number is half the difference between the given sum (72) and difference (26). This is the generic solution to a "sum and difference" problem. The smaller number is always half the difference of the give sum and difference. (Similarly, the larger is always half the sum of the given sum and difference.)
That is, the two numbers are always half the sum ± half the difference:
72/2 ± 26/2 = {36+13, 36-13} = {49, 23}
Answer:
C
Step-by-step explanation:
The secant- tangent angle MLK is half the difference of the intercepted arcs, that is
(KN - KM) = 70° ( multiply both sides by 2 to clear the fraction )
KN - KM = 140°
KN - 61° = 140° ( add 61° to both sides )
KN = 201° → C
Answer:
The 2nd option is correct
Step-by-step explanation:
The only numbers on a dice greater than 4 are 5 and 6, and we want to get the color blue, so the 2nd option is correct.
