Refer to figure 1 (see attached) for the initial drawing. The observation points are at A and B. I placed point A south of point B. The ship is at point C. I added in a compass as well.
As shown in figure 1, angle A is 33 degrees. You start by facing north and then you turn to face the eastward direction by 33 degrees. Angle B is 58 degrees. You start by facing south and then you turn 58 degrees to the east. The distance from A to B is 17 miles. Let's make c = 17. The lowercase c is opposite the upper case point C. Similarly, lowercase 'a' is opposite uppercase A; lowercase b is opposite uppercase B.
Once you have everything drawn out as shown in figure 1, we can use this info to find angle C
The three angles A,B,C add to 180 degrees
A+B+C = 180
33+58+C = 180
91+C = 180
91+C-91 = 180-91
C = 89
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Now use the law of sines to find the length of segment 'a'
a/sin(A) = c/sin(C)
a/sin(33) = 17/sin(89)
a = sin(33)*(17/sin(89))
a = 9.26027397983573
a = 9.3
Do the same for segment b
b/sin(B) = c/sin(C)
b/sin(58) = 17/sin(89)
b = sin(58)*(17/sin(89))
b = 14.419013720289
b = 14.4
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See figure 2 (attached) to see the fully solved triangle. When I refer to "solved triangle", I mean that we have found all of its sides and angles. In this case we have...
Angles:
A = 33 degrees
B = 58 degrees
C = 89 degrees
Sides:
a = 9.3 miles
b = 14.4 miles
c = 17 miles
Final answers are roughly 9.3 miles and 14.4 miles.
Answer: 4(2x²+9) or
Step-by-step explanation:
To solve the equation by factoring, we want to set the equation to zero. In order to have the equation equal to zero, we want to add both sides by 36.
8x²=-36 [add both sides by 36]
8x²+36=0
When it comes to factoring, we want to pull out numbers or variables that are common in each term.
8x²+36=0 [take out a 4 in each term]
4(2x²+9)=0
It may seem that 2x²+9 can be factored further, it actually can't. This tells us that the factored form of the equation is 4(2x²+9)=0.
To solve the equation, we want to find the value of x. We already know the graph does not cross the x-axis because the y-intercept or vertex is (0,9).
4(2x²+9)=0 [divide both sides by 4]
2x²+9=0 [subtract both sides by 9]
2x²=-9 [divide both sides by 2]
x²=-9/2 [square root both sides]
or
Answer:
$60
Step-by-step explanation:
John's Money = $2000
Annual Interest Rate = 6%
Total amount John should
receive after a year = 2000x(1+0.06)
= 2120
Total interest amount in a year = 2120 - 2000
= $120
Total interest amount in a per month = 120/12 = $10
Total interest amount in 6 months = 10 x 6 = $60