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QuestionHow many degrees must a gate arm move from 42∘42^{\circ} to reach a horizontal position?

Studdy Solution

STEP 1

Assumptions1. The arm starts from a vertical position. . The arm has moved 42∘42^{\circ} from the vertical position.
3. The arm needs to reach a horizontal position.
4. A full circle is 360∘360^{\circ}.
5. A right angle, or the angle between vertical and horizontal, is 90∘90^{\circ}.

STEP 2

First, we need to find the total degrees the arm needs to move to reach a horizontal position from a vertical position. Since a right angle is 90∘90^{\circ}, the total degrees required is 90∘90^{\circ}.
Total degrees=90∘Total\, degrees =90^{\circ}

STEP 3

Next, we need to subtract the degrees the arm has already moved from the total degrees required. This will give us the remaining degrees the arm needs to move to reach a horizontal position.
Remaining degrees=Total degrees−Moved degreesRemaining\, degrees = Total\, degrees - Moved\, degrees

STEP 4

Now, plug in the given values for the total degrees and moved degrees to calculate the remaining degrees.
Remaining degrees=90∘−42∘Remaining\, degrees =90^{\circ} -42^{\circ}

STEP 5

Calculate the remaining degrees the arm needs to move.
Remaining degrees=90∘−42∘=48∘Remaining\, degrees =90^{\circ} -42^{\circ} =48^{\circ}The arm needs to move 48∘48^{\circ} more to reach a horizontal position.

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