The professional basketball player was much taller anyone else in the room. Everyone kept staring at him in awe me. You see, I'm
2 answers:
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The height of the tree, which Pat needs to determine, before cutting it down to be sure that it will not fall on a nearby fence is 111 ft.
<h3>What is right angle triangle property?</h3>In a right angle triangle, the ratio of the opposite side to the base side is equal to the tangent angle between them.
Here, (b) is the opposite side, (a) is the base side.
Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence.
The angle of elevation of the tree from one position on a flat path from the tree is
From a second position,
Farther along this path it is,
Let the distance between tree and first position is x. Thus, from the trigonometry,
....1
The distance between tree and second position is (x+60) ft. Thus, again from the trigonometry,
......2
Compare the equation 1 and 2,
Put this value in equation 1 as,
Thus, the height of the tree, which Pat needs to determine, before cutting it down to be sure that it will not fall on a nearby fence is 111 ft.
Learn more about the right angle triangle property here;
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Answer:
a. 99.30% of the woman meet the height requirement
b. If all women are eligible except the shortest 1% and the tallest 2%, then height should be between 58.32 and 68.83
Explanation:
<em>According to the survey</em>, women's heights are normally distributed with mean 63.9 and standard deviation 2.4
a)
A branch of the military requires women's heights to be between 58 in and 80 in. We need to find the probabilities that heights fall between 58 in and 80 in in this distribution. We need to find z-scores of the values 58 in and 80 in. Z-score shows how many standard deviations far are the values from the mean. Therefore they subtracted from the mean and divided by the standard deviation:
z-score of 58 in= = -2.458
z-score of 80 in= = 6.708
In normal distribution 99.3% of the values have higher z-score than -2.458
0% of the values have higher z-score than 6.708. Therefore 99.3% of the woman meet the height requirement.
b)
To find the height requirement so that all women are eligible except the shortest 1% and the tallest 2%, we need to find the boundary z-score of the
shortest 1% and the tallest 2%. Thus, upper bound for z-score has to be 2.054 and lower bound is -2.326
Corresponding heights (H) can be found using the formula
and
Thus lower bound for height is 58.32 and
Upper bound for height is 68.83