A conveyor belt carries supplies from the first floor to the second floor, which is 27 feet higher. The belt makes a 60° angle with the ground. How far do the supplies travel from one end of the conveyor belt to the other? Round your answer to the nearest foot. If the belt moves at 75 ft/min, how long, to the nearest tenth of a minute, does it take the supplies to move to the second floor?

Question

mathstudent55 · Answer

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mathstudent55 · Answer

In a 30-60-90 triangle, the ratio of the lengths of the sides is:
1 : sqrt(3) : 2

anonymous · Answer

just do sin(60)=27/x

anonymous · Answer

multiply both sides by x
then divide both sides by sin(60) to get your answer

anonymous · Answer

then take that answer and divide it by 75

mathstudent55 · Answer

Here, the 27 ft side corresponds to the sqrt(3) side, and 
         the unknown side corresponds to 2
27/sqrt(3) = x/2

anonymous · Answer

how would i put that into the calculator??

mathstudent55 · Answer

You solve the proportion by cross multiplying:
27/sqrt(3) = x/2
xsqrt(3) = 2*27
x = 2*27/sqrt(3)
2 times 27 divided by sqrt of 3

anonymous · Answer

31?

anonymous · Answer

is it 31?

mathstudent55 · Answer

correct

anonymous · Answer

thank you :)