Answer: The required equation is
Thus, there are 71 students on the bus at the beginning of the route.
Step-by-step explanation:
Given: The number of students dropped off =
The number of students remain on the bus =
Let 'x' be the total number of students in the bus then we get the equation as
On adding 23 to 48, we get 71
Hence,
Therefore, There are 71 students on the bus at the beginning of the route.
Consult the attached diagram.
In the larger triangle,
tan(16°) = (7250 ft) / (<em>x</em> + <em>y</em>)
and in the smaller triangle,
tan(26°) = (7250 ft) / <em>y</em>
You want to solve for <em>x</em>.
From the first equation (I'm ignoring units from here on, all distances are measured in ft), you have
(<em>x</em> + <em>y</em>) tan(16°) = 7250
<em>x</em> tan(16°) + <em>y</em> tan(16°) = 7250
<em>x</em> tan(16°) = 7250 - <em>y</em> tan(16°)
<em>x</em> = 7250 cot(16°) - <em>y</em>
<em />
From the second equation,
<em>y</em> = 7250 cot(26°)
Solving for <em>x</em> gives
<em>x</em> = 7250 cot(16°) - 7250 cot(26°)
<em>x</em> = 7250 (cot(16°) - cot(26°))
<em>x</em> ≈ 10,433 ft
