A guy wire makes a 67° angle with the ground. Walking out 32 feet further from the tower, the angle of elevation to the top of t
he tower is 39°. Find the height of the tower.
1 answer:
Answer:
20.9 feet
Step-by-step explanation:
<em>The figure attached below can be formed through the information given.</em>
<u>Step 1: Find angle y</u>
<em>All angles of a triangle are equal to 180°</em>
<em>67 + 39 + y = 180</em>
<em>y = 74°</em>
<u>Step 2: Use sin formula to find H</u>
<em>a/sin a = b/sin b</em>
<em>32/sin 74 = b/sin 39</em>
b = 20.9 feet.
The height of the tower is 20.9 feet.
!!
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The question is an illustration of composite functions.
- Functions c(n) and h(n) are
and
- The composite function c(n(h)) is
- The value of c(n(100)) is
- The interpretation is: <em>"the cost of working for 100 hours is $130000"</em>
The given parameters are:
- $5000 in fixed costs plus an additional $250
- 5 systems in one hour of production
<u>(a) Functions c(n) and n(h)</u>
Let the number of system be n, and h be the number of hours
So, the cost function (c(n)) is:
This gives
The function for number of systems is:
<u>(b) Function c(n(h))</u>
In (a), we have:
Substitute n(h) for n in
Substitute
<u>(c) Find c(n(100))</u>
c(n(100)) means that h = 100.
So, we have:
<u>(d) Interpret (c)</u>
In (c), we have:
It means that:
The cost of working for 100 hours is $130000
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