## 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 grou

Question

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 4 options: 37 ft; 22.5 min 30 ft; 0.4 min 45 ft; 37 min 15 ft; 1.1 min

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1 week 2021-10-10T18:40:06+00:00 2 Answers 0

1. 30ft

2. 0.4 min

Step-by-step explanation:

In this question, apply sine law which states that sine Ф= opposite/hypotenuse

The general formulae; is SOHCAHTOA where ;

In the question the height of the two floors is the ” c” and the angel at the base is 60° and distance the conveyor travels is the hypotenuse

Hence; If 75ft=1min

30ft=?……………………simple math

30/75 = 0.4 minutes

i) 30 ft

ii) 0.4 min

Step-by-step explanation:

i)

The question will be modeled by a right-angled triangle where-by;

The length of the conveyor belt will represent the Hypotenuse

The vertical distance which is 26 feet high will be the Opposite side to the angle the belt makes the ground which is given as 60 degrees.

The horizontal distance which is the ground will be the Adjacent side to the angle 60 degrees.

Therefore, we have a right angled triangle in which one angle and the length of the opposite side are given. To determine the length of the conveyor belt, the hypotenuse, we use the sine definition of an acute angle;

Remember the mnemonic. SOHCAHTOA

sine 60 = (opposite side)/(hypotenuse)

Hypotenuse = (opposite side)/sin 60

Hypotenuse = 26/sin 60

Hypotenuse = 30.02

The supplies thus travel 30 ft from one end of the conveyor belt to the other.

ii)

The speed of the belt is given as 75 ft/min

The length of the belt has been found to be approximately 30 ft

We are required to determine the time it takes for the supplies to move to the second floor.

Distance, Time and speed are related according to the following equation;

Distance = Time * Speed

Time = Distance/Speed

Time = 30/75

Time = 0.4 min