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15 Aug 2019, 00:02
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A road declines 30° from horizontal over a distance of 60 feet, as measured by a tape on the road's surface. At the base of the incline is a hole 7 feet deep. What is the difference in elevation between the top of the incline and the bottom of the hole?
A. 126
B. 37
C. 23
D. \(7 + 60\sqrt{3}\)
E. \(7 + 30\sqrt{3}\)
A. 126
B. 37
C. 23
D. \(7 + 60\sqrt{3}\)
E. \(7 + 30\sqrt{3}\)
15 Aug 2019, 00:46
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Angle of decline made with the horizontal is 30, meaning angle of decline made with the vertical is 60.
We know from the question stem that the declined road is 60ft long.
The vertical distance of the inclined road can be obtained as follows: 60sin30 or 60cos60 = 30ft.
Distance from the start of the decline to the bottom of the hole = 7+30 = 37ft.
Answer imo is B.
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We know from the question stem that the declined road is 60ft long.
The vertical distance of the inclined road can be obtained as follows: 60sin30 or 60cos60 = 30ft.
Distance from the start of the decline to the bottom of the hole = 7+30 = 37ft.
Answer imo is B.
Posted from my mobile device
15 Aug 2019, 08:08
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Bunuel
A road declines 30° from horizontal over a distance of 60 feet, as measured by a tape on the road's surface. At the base of the incline is a hole 7 feet deep. What is the difference in elevation between the top of the incline and the bottom of the hole?
A. 126
B. 37
C. 23
D. \(7 + 60\sqrt{3}\)
E. \(7 + 30\sqrt{3}\)
A. 126
B. 37
C. 23
D. \(7 + 60\sqrt{3}\)
E. \(7 + 30\sqrt{3}\)
the length of decline is 60 ft and angle corresponding to it is 90 ; we get a 30:60:90 ; so the height of decline ; 30 feet
base of incline would be the point at the end of 60 feet decline dip ; which is 7 feet
so difference between top of incline and bottom of hole ; 30-7 ;23 feet
IMO C
