Answer:
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 ;
(SOH) sineФ=opposite/hypotenuse ; (COH) cosine Ф= adjacent/hypotenuse and (TOA) tan Ф=opposite/adjacent
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;
[tex]Sin 60= \frac{26}{H} \\\\\\H=\frac{26}{Sin60} \\\\\\H=30 ft[/tex]
If 75ft=1min
30ft=?........................simple math
30/75 = 0.4 minutes
Answer:
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
