In the right triangle shown, m\angle A = 30\degreem∠A=30°m, angle, A, equals, 30, degree and AB = 12\sqrt{3}AB=12
2 answers:
Answer: Line AC = 24 units and line BC = 12 units.
Step-by-step explanation: Please refer to the diagram attached for more details.
The right angled triangle ABC has been drawn with angle A measuring 30 degrees and line AB measuring 12√3. To calculate the other two unknown sides AC labelled b, and BC labelled a, we shall use the trigonometric ratios. However, in this scenario, we shall apply the special values of each trigonometric ratio. These are shown in the box on the top right in the picture. The proof is given in the second right angled triangle at the bottom part of the attached picture.
Assume an equilateral triangle with lengths 2 units on all sides and 60 degrees at all angles. Drawing a line perpendicular to the bottom line would divide the top angle into two equal halves (30 degrees each), and the bottom line also would be divided into two equal halves (1 unit each). So the hypotenuse will measure 2 units and the line at the base would measure 1 unit. By using the Pythagoras' theorem, we derive the third side to be √3 <u>(that is x² = 2² - 1², and then x² = 4 - 1, and then x² = 3 and finally x = √3).</u>
Therefore, in triangle ABC, using angle 30 as the reference angle, to calculate side AC;
Cos 30 = Adjacent/Hypotenuse
Cos 30 = (12√3)/b
b = (12√3)/Cos 30
Where Cos 30 is √3/2
b = (12√3)/√3/2
b = (12√3) * 2/√3
b = 12 * 2
b = 24
To calculate side BC;
Tan 30 = Opposite/Adjacent
Tan 30 = a/(12√3)
Tan 30 * 12√3 = a
Where Tan 30 = 1/√3
(1/√3) * 12√3 = a
12 = a
Therefore, the missing lengths in the right triangle are
AC = 24 units and BC = 12 units
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Answer:
So the p value obtained was a very low value and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of interest is significantly higher than 0.012 (1.2%)
Step-by-step explanation:
Data given and notation
n=1655 represent the random sample taken
estimated proportion of interest
is the value that we want to test
represent the significance level
Confidence=99% or 0.99
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that true proportions is higher than 0.012.:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statisitic, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided . The next step would be calculate the p value for this test.
Since is a right tailed test the p value would be:
So the p value obtained was a very low value and using the significance level given we have
so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 1% of significance the proportion of interest is significantly higher than 0.012 (1.2%)