What is the angle of elevation of the sun when a pole 32.0 ft tall casts a shadow 45.0 ft long
1 answer:
As you can see in the first drawing, the vertical line represents the pole which is 32.0 ft long and the horizontal line represents the shadow casted by the pole which is 45.0 ft long. The angle θ, represents the angle of elevation of the sun.
We can solve this problem using trigonometric ratios, that is sine, cosine, and tangent. Remember SOH CAH TOA?
SOH
CAH
TOA
In this case, we're going to use TOA since we are given the height of the pole which represents the line opposite the angle of elevation, and the length of the shadow of the pole which represents the line adjacent to the angle of elevation.
adjacent, a = 45.0
opposite, o = 32.0
So, to find the angle of elevation, refer to the second picture above.
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Answer:
a) There is a 15.3% probability that a randomly selected person in this country is 65 or older.
b) Given that a person in this country is uninsured, there is a 2.2% probability that the person is 65 or older.
Step-by-step explanation:
We have these following percentages:
5.3% of those under the age of 18, 12.6% of those ages 18–64, and 1.3% of those 65 and older do not have health insurance.
22.6% of people in the county are under age 18, and 62.1% are ages 18–64.
(a) What is the probability that a randomly selected person in this country is 65 or older?
22.6% are under 18
62.10% are 18-64
The rest are above 65
So
100% - (22.6% + 62.10%) = 15.3%
There is a 15.3% probability that a randomly selected person in this country is 65 or older.
b) Given that a person in this country is uninsured, what is the probability that the person is 65 or older?
This can be formulated as the following problem:
What is the probability of B happening, knowing that A has happened.
It can be calculated by the following formula
Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.
So, what is the probability that a person is 65 and older, given that the person is uninsured.
P(B) is the probability that a person is 65 and older. From a), we have that
P(A/B) is the probability is uninsured, given that that person is 65 and older. So
P(A) is the probability that a person is uninsured. That is the sum of 5.3% of 22.6%, 12.6% of 62.1% and 1.3% of 15.3%. So:
So
Given that a person in this country is uninsured, there is a 2.2% probability that the person is 65 or older.