Sin α = 12/13 opposite/hypothenue
cos α = 5/13 adjacent/hypothenue
tan α = 12/5 opposite/adjacent
Answer:
2.10 s, 10.40 s.
Step-by-step explanation:
We know that the height of the rocket is given by the function:
We are asked to find the time for which the height of the rocket will be 350 ft. So, for that moment, we know the height but we don't know the time; however, we know that the equation can help us to find the time, doing h=350:
The last is a quadratic equation, which can be put in the form 
and solved applying the formula:
So, let's put the equation on the form adding 
and subtracting 
to each side of the equation; the result is:
So, we note that a=16, b=-200, and c=350.
Then,
According to the equation, that are the times for which the height will be 350 ft; that is because the rocket is going to ascend and then to fail again to the ground.
Before we begin, let's identify what kind of angles these are and are they related in any way?
These angles are both acute and they are both corresponding angles.
Corresponding angles are equal to each other, and we can use this fact to our advantage.
Since they are equal to each other, we can set the equations of 1 and 2 equal to each other. Like so,
1 = 2
83 - 2x = 92 - 3x
Now, we can solve for X by isolating it on one side.
83 - 2x = 92 - 3x
Add 3x to each side: (This basically moves the X on the right side to the left.)
83 - 2x + 3x = 92 - 3x + 3x
83 + x = 92
Subtract 83 on each side to isolate the X.
83 + x - 83 = 92 - 83
x = 92 - 83
x = 9
Therefore, X equals 9. To check our work, we can substitute X for 9.
83 - 2(9) = 92 - 3(9)
83 - 18 = 92 - 27
65 = 65 -
TRUE
So to conclude, Angle 1 is 65 degrees, Angle 2 is 65 degrees, and X equals 9.
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