help with trigonometric ratios?
PROBLEM A: A submarine is traveling parallel to the surface of the water 626 meters below the surface. The sub begins a constant ascent to the surface so that it will emerge on the surface after traveling 4420 meters from the point of its initial ascent.
1. what angle of ascent did the submarine make?
2. what horizontal distance did the submarine travel during its ascent?
PROBLEM B: Germaine pilots a small plane on weekends. During a recent flight, he determined that he was flying at an altitude of 3000 feet parallel to the ground and that the ground distance to the start of the landing strip was 8000 feet.
1. What is Germaines angle of depression to the start of the landing strip?
2. What is the distance between the plane in the air and the landing strip on the ground.
PROBLEM C: Leonard and Alecia are building a new feed storage system on their farm. The feed conveyor must be able to reach a range of of heights. It has a length of 8 meters, and its angle of elevation can be adjusted from 20degrees to 5degrees. Under these conditions, what range of heights is possible for an opening in the builing through with feed can pass?
THANKS SO MUCH FOR ALL THE HELP YOU SMARTICLE PEOPLE 
August 29th, 2011 at 9:37 am
PROBLEM A
1. The angle of ascent :
You can find the angle “X” with the sine :
sin(X) = 626 / 4420
X = sin^-1(626/4420) = 8.142 degrees
note : On the Windows calculator, you can find sin^-1 by choosing the option “Inv” and press the sine key.
2. Horizontal distance :
We can use either the cosine or the tangent :
cos(8.142) = x / 4420
x = 4420 * cos(8.142)
x = 4375.5 meters
or
tan(8.142) = 626 / x
x = 626 / tan(8.142)
x = 4375.5 meters
PROBLEM B
1. Angle of depression :
We can find the angle by the tangent :
tan(X) = 3000 / 8000 = 3/8
X = tan^-1(3/8) = 20.556 degrees
2. Distance between the plane in the air and the landing strip on the ground
It is the hypotenuse of the triangle.
Pythagorus law :
x^2 = 3000^2 + 8000^2
x = sqrt(3000^2 + 8000^2)
x = 8544 feet
You can also find it by the sine or the cosine :
sin(20.556) = 3000 / x
x = 3000 / sin(20.556) = 8544 feet
cos(20.556) = 8000 / x
x = 8000 / cos(20.556) = 8544 feet
PROBLEM C
Angle of 5 degrees :
sin(5) = height / 8
height = 8 * sin(5)
height = 0.697 meter
Angle of 20 degrees :
sin(20) = height / 8
height = 8 * sin(20)
height = 2.736 meters
Range is from 0.697 meter to 2.736 meters
20 Jan 2013
THE COUNTDOWN IS ON!!!!
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