From the top of a tower, an object which is 97 m away from the base of the tower, is at a 37° angle of depression.
1 answer:
<h3>Answer: 73</h3>
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Work Shown:
Check out the diagram below. Note the pair of alternate interior angles that are congruent (each 37 degrees). Then focus on triangle ABC. With the reference angle being at A, this means we use the tangent function because BC = x is the opposite side and AB = 97 is the adjacent side.
tan(angle) = opposite/adjacent
tan(A) = BC/AB
tan(37) = x/97
97*tan(37) = x
x = 97*tan(37)
x = 73.094742859971
For the last step, you'll need a calculator that can handle trig functions. Make sure the calculator is in degree mode. The result here is approximate. This rounds to 73 when rounding to the nearest whole number.
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Answer:
a) "=T.INV(0.025,10)" and "=T.INV(1-0.025,10)"
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b) "=T.INV(0.025,20)" and "=T.INV(1-0.025,20)"
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c) "=T.INV(0.005,20)" and "=T.INV(1-0.005,20)"
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d) "=T.INV(0.005,50)" and "=T.INV(1-0.005,50)"
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e) "=T.INV(1-0.01,25)"
And we got
f) "=T.INV(0.025,5)"
And we got
Step-by-step explanation:
Previous concepts
The t distribution (Student’s t-distribution) is a "probability distribution that is used to estimate population parameters when the sample size is small (n<30) or when the population variance is unknown".
The shape of the t distribution is determined by its degrees of freedom and when the degrees of freedom increase the t distirbution becomes a normal distribution approximately.
The degrees of freedom represent "the number of independent observations in a set of data. For example if we estimate a mean score from a single sample, the number of independent observations would be equal to the sample size minus one."
Solution to the problem
We will use excel in order to find the critical values for this case
Determine the t critical value(s) that will capture the desired t-curve area in each of the following cases:
a. Central area =.95, df = 10
For this case we want 0.95 of the are in the middle so then we have 1-0.95 = 0.05 of the area on the tails. And on each tail we will have .
We can use the following excel codes:
"=T.INV(0.025,10)" and "=T.INV(1-0.025,10)"
And we got
b. Central area =.95, df = 20
For this case we want 0.95 of the are in the middle so then we have 1-0.95 = 0.05 of the area on the tails. And on each tail we will have .
We can use the following excel codes:
"=T.INV(0.025,20)" and "=T.INV(1-0.025,20)"
And we got
c. Central area =.99, df = 20
For this case we want 0.99 of the are in the middle so then we have 1-0.99 = 0.01 of the area on the tails. And on each tail we will have .
We can use the following excel codes:
"=T.INV(0.005,20)" and "=T.INV(1-0.005,20)"
And we got
d. Central area =.99, df = 50
For this case we want 0.99 of the are in the middle so then we have 1-0.99 = 0.01 of the area on the tails. And on each tail we will have .
We can use the following excel codes:
"=T.INV(0.005,50)" and "=T.INV(1-0.005,50)"
And we got
e. Upper-tail area =.01, df = 25
For this case we need on the right tail 0.01 of the area and on the left tail we will have 1-0.01 = 0.99 , that means
We can use the following excel code:
"=T.INV(1-0.01,25)"
And we got
f. Lower-tail area =.025, df = 5
For this case we need on the left tail 0.025 of the area and on the right tail we will have 1-0.025 = 0.975 , that means
We can use the following excel code:
"=T.INV(0.025,5)"
And we got