Answer:
Angle of Depression and Angle of Elevation
One application of the trigonometric ratios is to find lengths that you cannot measure. Very frequently, angles of depression and elevation are used in these types of problems.
Angle of Depression: The angle measured down from the horizon or a horizontal line.
Angle of Elevation: The angle measured up from the horizon or a horizontal line.
What if you placed a ladder 10 feet from a haymow whose floor is 20 feet from the ground? How tall would the ladder need to be to reach the haymow's floor if it forms a 30∘ angle with the ground?
Let's call a child's ticket
and an adult's ticket
. From this, we can say:
,
since 116 tickets are sold in total.
Now, we are going to need to find another equation (the problem asks us to solve a systems of equations). This time, we are not going to base the equation on ticket quantity, but rather ticket price. We know that an adult's ticket is $17,000, and a child's ticket is thus
.
Given these values, we can say:
,
since each adult ticket
costs 17,000 and each child's ticket
costs 12,750, and these costs sum to 1,653,250.
Now, we have two equations:


Let's solve:


- Find
on its own, which will allow us to substitute it into the first equation

- Substitute in
for 

- Apply the Distributive Property


- Subtract 1972000 from both sides of the equation and multiply both sides by -1

We have now found that 75 child's tickets were sold. Thus,
,
41 adult tickets were sold as well.
In sum, 41 adult tickets were sold along with 75 child tickets.
Multiply both sides by 4
subtract 24r from both sides
simplify r - 24r to -23r
divide both sides by -23
two negatives make a positive
simplify 14/5/23 to 14/5 x 23
simplify 5 x 23 to 115
switch sides
Answer: r = 14/115.