A conveyor belt carries supplies from the first floor to the second floor, which is 26 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

Tristian Stanley

Mathematics

9 November, 22:34

A conveyor belt carries supplies from the first floor to the second floor, which is 26 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?

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Answers (1)

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Karson Joyce · Answer 1

30 ft; 0.4 min

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you ...

... Sin = Opposite/Hypotenuse

Here, the angle of elevation is opposite the triangle side representing the distance between floors. The hypotenuse is the length of the conveyor belt. Rearranging the formula (by muliplying by Hypotenuse/Sin), we get ...

... Hypotenuse = Opposite/Sin

Filling in the values from this problem, we have ...

... length of conveyor = (26 ft) / sin (60°) ≈ 30 ft

The time it takes to travel that distance is given by ...

... time = distance/speed

... time = (30 ft) / (75 ft/min) = 2/5 min = 0.4 min