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The value of two arithmetic means which are inserted between 3 and 24 are 24/9 and 75/9.
<h3>What is arithmetic mean?</h3>Arithmetic mean is the mean or average which is equal to the ratio of sum of all the group numbers to the total numbers.
The two arithmetic means between 3 and 24 are has to be inserted.
3, A₂, A₃, 24
All the four numbers are in arithmetic progression. The nth terms of AM can be found using the following formula:
t(n)=a(n-1)d
Here, d is the common difference a is the first terms and n is the total term. The first term, a=3 and t₄=24. Thus, the common difference is;
The second and 3rd term are:
Thus, the value of two arithmetic means which are inserted between 3 and 24 are 24/9 and 75/9.
Learn more about the arithmetic mean here;
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We need to solve for the height of the tree given two angles and distance between the two observers. See attached drawing for a better understanding of the problem.
We derive to equations using SOH CAH TOA such as below:
sin30 = h / x
sin 45 = h / (100-x)
sin 45 (100-x) = xsin30
70.71 - 0.71x = 0.5x
70.71 = 1.21 x
x = 58.44
Solving for h, we have:
h = xsin30
h = 58.44 sin30
h = 29.22
The height of the tree is 29.22 feet.
We derive to equations using SOH CAH TOA such as below:
sin30 = h / x
sin 45 = h / (100-x)
sin 45 (100-x) = xsin30
70.71 - 0.71x = 0.5x
70.71 = 1.21 x
x = 58.44
Solving for h, we have:
h = xsin30
h = 58.44 sin30
h = 29.22
The height of the tree is 29.22 feet.