Triangle ABC has AB = 10 √3cm, AC=6cm and has area 45cm^2
(i) Find the size of angle CAB.
(ii) Find the length of BC
Answers
Answer:
I) ∠CAB measures 60°.
II) BC measures approximately 15.23 cm.
*Please read notes.
Step-by-step explanation:
We are given ΔABC, where AB measures 10√3 cm, AC measures 6 cm, and the triangle has an area of 45 square cm.
And we want to find I) the measure of ∠CAB and II) the length of BC.
I) First, we should always draw a representative triangle so we can determine the sides and angles. This is shown below.
Note that ∠CAB (or simply ∠A) is the angle between the two sides. Thus, we can find the angle by using the alternative formula for the area of a triangle:
[tex]\displaystyle A=\frac{1}{2}ab\sin(C)[/tex]
Where a and b are two side lengths, and C is the angle between the two sides.
Substitute:
[tex]\displaystyle 45=\frac{1}{2}(10\sqrt{3})(6)\sin(A)[/tex]
Simplify:
[tex]\displaystyle 45=30\sqrt{3}\sin(A)[/tex]
So:
[tex]\displaystyle \sin(A)=\frac{45}{30\sqrt{3}}=\frac{3}{2\sqrt3}=\frac{\sqrt{3}}{2}[/tex]
Take the inverse sine of both sides. Use a calculator. Thus:
[tex]\displaystyle m\angle A=\sin^{-1}\left(\frac{\sqrt{3}}{2}\right)=60^\circ[/tex]
II) To find BC, we will use the Law of Cosines. We do not know whether or not ΔABC is a right triangle, so we cannot use right triangle trigonometry or special right triangles.
The law of cosines is:
[tex]\displaystyle c^2=a^2+b^2-2ab\cos(C)[/tex]
Where a and b are side lengths and C is the angle between the side lengths. c is the side length opposite to the angle.
BC is opposite to A. Substitute:
[tex](BC)^2=(10\sqrt{3})^2+(6)^2-2(10\sqrt{3})(6)\cos(60^\circ)[/tex]
Simplify:
[tex]\displaystyle BC^2=336-120\sqrt{3}\left(\frac{1}{2}\right)=336-60\sqrt{3}[/tex]
Take the square root of both sides:
[tex]\displaystyle BC=\sqrt{336-60\sqrt{3}}\approx 15.23[/tex]
BC measures about 15.23 cm.
Notes:
In this case, the inverse sine of √3/2 will yield two answers: 60° and 120°. This is an example of an ambiguous case. Both of these angles will work. However, BC will be different. If ∠A is 60°, then BC is about 15.23. However, if ∠A is 120°, then BC is about 20.97. Both will result in the triangle having an area of 45 square cm, as well as AB measuring 10√3 and AC measuring 6.
Related Questions
Simplify by adding like terms: 2abab - 4ba^2b + 7ab^a + 3a^2b
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The Ericsson method is one of several methods claimed to increase the likelihood of a baby girl. In a clinical trial, results could be analyzed with a formal hypothesis test with the alternative hypothesis of p>0.5, which corresponds to the claim that the method increases the likelihood of having a girl, so that the proportion of girls is greater than 0.5. If you have an interest in establishing the success of the method, which of the following P-values would you prefer: 0.999, 0.5, 0.95, 0.05, 0.01, 0.001? Why? The P-value of (0.999.05.095.005-001.0001) 2 is preferred because it corresponds to the sample evidence that most strongly supports the (null/ altenative)? hypothesis that the method (is/ is not)? effective.
Answers
Answer:
0.001
Step-by-step explanation:
Ericsson is claimed to increase the likelihood of a baby girl ;
Given the alternative hypothesis to buttress this claim :
HA : p>0.5
In other to establish the success of Ericsson's claim, then there must be significant evidence to reject the Null hypothesis ; hence adopt the alternative.
To Do this, we need a very small Pvalue ; such that it will be lesser than the α - value in other to reject the Null and adopt the alternative.
Recall ;
Pvalue < α ; We reject the Null
Therefore, from the options, we choose the smallest Pvalue as we want the Pvalue to be as small as possible.
A 12 foot ladder is placed 3 feet from a house and leaned against the house. At what height does the ladder touch the house?
Answers
The population of a town is 4,000 people. Every year the population increases by 4%. What will the population of this town be after 7 years?
After 7 years the population of this town will be?
Answers
Answer:
The answer is 5,120
Step-by-step explanation:
How to find 4% of 4000:
4 times 4000=
16000 divided by 100
160
Then you add 160 to 4000 7 times and you get 5,120.
Answer:
p=c(1+r)^t the population in 7 years will be 5263.72711694
Step-by-step explanation:
p=c(1+r)^t
p=4,000(1+.04)^t
p=4,000(1.04)^t
p=4,000(1.04)^4
p=4679.43424
p= the population you are solving for
c= the initial amount of the population
(1+r)= the rate of change
t= the period of time
2(x-3)-5 equal to or less than 9
Answers
Answer:
x ≤ 10
Step-by-step explanation:
2x-6-5 ≤ 9
2x-11 ≤ 9
2x ≤ 20
x ≤ 10
giving brainliest 3x^{2} -5x-2=0
Answers
Answer:
Step-by-step explanation:
I can guess what the instructions are, but it'd be helpful if you were to share them.
3x^2 - 5x - 1 = 0 is a quadratic with coefficients {3, -5, -1}. Find the discriminant b^2 - 4ac: 25 - 4(3)(-1) = 13.
Because the discriminant is positive, we know we have two unequal real roots here. Continuing with the quadratic formula, we obtain:
-(-5) ±√13 5 ± √13
x = ----------------- = ----------------
2(3) 6
Answer:
4x=2
Step-by-step explanation:
3x^2-5x-2=0
9x-5x-2=0
4x +2 +2
4x=2
5)
Which fraction is equivalent to 1/4
A 2/6 b 4/16 c 4/1 d 4/8
Answers
Tyler has a stack of cards. He picks a card, records the color, and returns the card to the stack. He repeats this 60 times and chooses a red card 24 times. What is the experimental probability of choosing a red card from the stack?
Answers
Answer:
24/60 = 2/5
Step-by-step explanation: dont have one
Answer:
2/5, or 40%
Step-by-step explanation:
The experimental probability is not what the mathematical probability of something always is of happening, but rather the probability based on the pattern of given data in a given experiment. So rather than giving the likelihood of picking a red card on the next pick, you would instead give the "likelihood" of picking a red card based on the trend found in the given data. This would amount to 24/60 which, simplified, would be 2/5, or 40%.
I would appreciate Brainliest, but no worries.
Rowenas new kitten weights 12 times as much as her hamster. The conbines weight of the kitten and thw hamster is 468 grams. What is the weight of the kitten
Answers
Answer: 36
Step-by-step explanation: 36x12=432
432+36=468
Will mark brainly
ASAP
Answers
Answer:
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I hope this helped!!
Calculate each value for ⊙P. Use 3.14 for π and round to the nearest tenth.
mJKL = 230
area of shaded sector =
area of unshaded sector =
Answers
Answer:
Area of the unshaded sector = 113.4 sq units
Area of the shaded sector = 200.6 sq units
Step-by-step explanation:
First let us calculate the area of the circle
Area of the circle = πr²
radius r = 10units
Area of the circle = π(10)²
Area of the circle = π(100)
Area of the circle = 3.14(100)
Area of the circle = 314 sq. units
Area of a sector = theta/360 * πr²
Area of the unshaded sector = 130/360 * 314
Area of the unshaded sector = 13/36 * 314
Area of the unshaded sector = 113.389 sq units
Area of the unshaded sector = 113.4 sq units
Area of the shaded sector = Area of circle - Area of the unshaded sector
Area of the shaded sector = 314 - 113.89
Area of the shaded sector = 200.6sq. units
Jessica has a coupon for 20% off the original price of
her purchase.
When she gets to the checkout counter, the employee
notifies her that they are going to take an additional
15% off the already reduced price.
What is the final price of a pair of sneakers that
originally cost $140?
Answers
Answer: $95.20
Step-by-step explanation:
140 * .2 = 28
140 - 28 = 112
112 * .15 = 16.8
112 - 16.8 = 95.2
Answer:
95.2
Step-by-step explanation:
hope it helps. that's the least I could do if it's not correct please tell me.
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Answers
Answer:
359.19
Step-by-step explanation:
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find the answer, 1/2 divided by 4
Answers
Answer:
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Which graph represents a function with a domain of all numbers greater than or equal to -7 and less than 2? Your explanation should include all information about reading domain on a graph given the limitations. As well as how the different circles affects the notation on the graph when equal to and not equal to are used.
Answers
Answer: D.
Step-by-step explanation:
The way to know if it is “greater than or equal to” opposed to jsut greater than is to look at the dot. If it is filled in it is “equal to” if not it isn’t.
4/5 - 1/10=
A. 7/10
B.3/5
C.3/10
D.2/25
Answers
Answer
A 7/10
Step-by-step explanation:
if you make it even, you double the 4/5 to make it a 8/10, if you every have a number that is like 4/6-2/18, you triple the 4 to make 12, and triple the 6 to make it 18. so you now have 12/18-2/18=10
So 8/10-1/10=7/10
What is angle m1 and angle m2?
Answers
Answer:
1) 122 2)58
Step-by-step explanation:
Answer:
m1 = 122°
m2 = 58°
Step-by-step explanation:
angle 1 = 122° rule of vertical angles
180° -122° = 58°
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
Find the sum of the zeros in the following equation: (2x-1)(x+8)(2x-4)(x-1)
Answers
Answer:
[tex]-9\frac{1}{2}[/tex]
Step-by-step explanation:
[tex]2x+1=0[/tex]
[tex]2x=-1[/tex]
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[tex]x+8=0[/tex]
[tex]x=-8[/tex]
[tex]2x-4=0[/tex]
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Answers
Answer:
453.33
Step-by-step explanation:
Ratios:
[tex]\frac{15}{100} =\frac{68}{x} \\\\15x=6800\\x=453.33[/tex]
Double check:
453.33(0.15) = 68
x
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Answer:
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will mark brainliest pls help
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I NEED HELP ON THIS ASAP!!!
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A. Plant C is 0.64 times as tall as Plant B
B. Plant C is 2.4 inches shorter than Plant B
Which quantity is proportional to 35⁄80?
Answers
Answer:
7/16
Step-by-step explanation:
Answer:
7/16
Step-by-step explanation:
Simplify
The graph shown meets the conditions -3 ≤ y ≤ 3.
True or False
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Answer:
true
Step-by-step explanation:
I NEED HELP I AM DESPERATE PLEASE JUST HELP ME
THE AREA IS ___ SQUARE UNITS
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Answer:
50 units
Step-by-step explanation:
First find the length and width by using distance formula.
QR = Square root of 25 =5
RS = Square root of 100 =10
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When Georgia started Kindergarden, her parents set aside $10,000 in an account that yielded 5.6% interest compounded annually to pay for her college tuition. After 6 years of elementary school, 3 years of middle school and 4 years of high school, how much was in the account for Georgia’s college tuition?
Answers
Answer:
17,280
Step-by-step explanation:
first, you find 5.6 % of 10,000 which is 560. Then you have to figure out how many years the interest was coming in which is 13 years. you multiply the 560 by 13 years to get 7,280 and add that to 10,000. that's how you get your final answer of 17,280
Don't have a question,Need help asap
Answers
Answer:
x = 31
m<ABC = 113
Step-by-step explanation:
The angles are supplementary.
x + 82 + x + 36 = 180
2x + 118 = 180
2x = 62
x = 31
m<ABC = x + 82 = 31 + 82 = 113
Answer:
x = 31
m<ABC = 113
Which of the following statements are true about the graph of f(x) = 6(x + 1)2 -9?
Check all of the boxes that apply.
a. The vertex is (1, -9).
b. The graph opens upward.
c. The graph is obtained by shifting the graph of f(x) = 6(x + 1)2 up 9 units.
d. The graph is steeper than the graph of f(x) = x2.
e. The graph is the same as the graph of f(x) = 6x2 + 12x - 3.
Answers
Answer:
Step-by-step explanation:
a. The vertex is (1, -9). False. The vertex is (-1, -9).
b. The graph opens upward. True. That coefficient '6' is positive.
c. The graph is obtained by shifting the graph of f(x) = 6(x + 1)2 up 9 units. False. It's DOWN 9 units.
d. The graph is steeper than the graph of f(x) = x^2. True. The given function increases 6 times faster than does x^2.
e. The graph is the same as the graph of f(x) = 6x2 + 12x - 3.
Let's put f(x) = 6(x + 1)^2 -9 into standard form. Expanding the first term, we get f(x) = 6(x^2 + 2x + 1) - 9, or f(x) = 6x^2 + 12x + 6 - 9. YES, TRUE
Irene knows there are 2 cups in 1 pint. She writes the equation c=2p to find the number of cups, c, in any number of pints, p. Use the drop-down menus to complete the statements about Irene's equation.
Answers
Answer:
See Explanation
Step-by-step explanation:
The question is incomplete, as there are no options to select from.
However, a general explanation is as follows.
Given
[tex]2\ cups = 1\ pint[/tex]
Required
Is [tex]c = 2p[/tex] a correct expression?
Let
[tex]c = cups[/tex]
[tex]p = pint[/tex]
So:
[tex]2\ cups = 1\ pint[/tex]
becomes
[tex]2 * c = 1 * p[/tex]
[tex]2c = p[/tex]
Divide both sides by 2
[tex]c =\frac{1}{2}p[/tex]
Hence:
[tex]c = 2p[/tex] is incorrect