ENGR. BESAVILLA’S NOTES
Problem 102 Problem 109
While still at a sizable distance from the Pentagon building, a man first A student beginning the study of Trigonometry came across an expression of
catches sight of it. Is he more likely to be able to see two sides or three? the form sin (X + Y). He evaluated this as sin X + sin Y. Surprisingly he was
correct. The values of X and Y differed by 10˚; what were these values,
Ans: Equal
assuming that 0˚ < X < Y < 360˚?
Ans: x = 175˚
Problem 103 y = 185˚
A pirate buried his treasure on an island, a conspicuous landmark of which
were three palm trees, each one 100 feet from the other two. Two of these
trees were in a N-S line. The directions for finding the treasure read: Problem 110
“Proceed from southernmost tree 15 feet due north, then 26 feet due west.” One side of the triangle is 10 feet longer than another and the angle between
Is the treasure buried within the triangle formed by the tree? them is 60˚. Two circles are drawn with these sides as diameters. One of the
points of intersection of the two circles is the common vertex. How far from
Ans: outside the triangle
the third side is the other point of intersection?
Ans: 0
Problem 104
An Origami expert started making a Nani-des-ka by folding the top left corner
of a sheet of paper until it touched the right edge and the crease passed Problem 112
through the bottom left corner. He then did the same with the lower right There is one flag at the entrance to a racetrack and another inside the track,
corner, thus making two slanting parallel lines. The paper was 25 inches long half a mile from the first. A jockey notes that no matter where he is on the
and the distance between the parallel lines was exactly 7/40 of the width. track, one flag is 3 times as far away as the other. How long is the track?
How wide was the sheet of paper?
Ans: 1980π
Ans: 24 inches
Problem 113
Problem 105 What is the longest 6’ wide shuffle board court which will fit in a 20’ x 30’
The Ben Azouli are camped at an oasis 45 miles west of Taqaba. They rectangular room?
decided to dynamite the Trans-Hadramaut railroad joining Taqaba to Ans: 30 7/8 ft.
Maqaba, 60 miles north of the oasis. If the Azouli can cover 18 miles a day,
how long will it take them to reach the railroad?
Problem 114
Ans: 2 days
Find the smallest number (x) of persons a boat may carry so that (n) married
couples may cross a river in such a way that no woman ever remains in the
Problem 106 company of any man unless her husband is present. Also find the least
number of passages (y) needed from one bank to the other. Assume that the
A yang, ying, and yung is constructed by dividing a diameter of a circle, AB,
boat can be rowed by one person only.
into three parts by points C and D, then describing on one side of AB
semicircles having AC and AD as diameters and on the other side of AB Ans: x = 2
semicircles having BD and BC as diameters. Which is larger, the central y=5
portion or one of the outside pieces?
Ans: Same
Problem 115
A, B and C participate in a track meet, consisting of at least three events. A
Problem 107 certain number of points are given for first place, a smaller number for
second place, and a still smaller number for third place. A won the meet with
A diaper is in the shape of a triangle with sides 24, 20 and 20 inches. The
a total score of 14 points; B and C are tied for second with 7 points apiece. B
long side is wrapped around the baby’s waist and overlapped two inches.
won first place in the high jump. Who won the pole vault assuming no ties
The third point is brought up to the center of the overlap and pinned in place.
occurred in any event?
The pin is to go through three thicknesses of material. What is the area in
which the pin may be placed? Ans: A
Ans: 2.5 in2
Problem 116
Maynard the Census Taker visited a house and was told, “Three people live
Problem 108 there. The product of their ages is 1296, and the sum of their ages is our
A hostess plans to serve a square cake with icing on top and sides. Upon house number.” After an hour of cogitation Maynard returned for more
determining how many guests want cake, what method should she use to information. The house owner said, “I forgot to tell you that my son and
insure that each guest will receive the same amount of cake and icing? grandson live here with me.” How old were the occupants and what was their
Ans: Top areas are equal to receive the same amount of cake. street number?
Side areas are equal to receive equal icing areas. Ans: age of occupants = 1 and 18, street number = 72
Problem 102 Problem 109
While still at a sizable distance from the Pentagon building, a man first A student beginning the study of Trigonometry came across an expression of
catches sight of it. Is he more likely to be able to see two sides or three? the form sin (X + Y). He evaluated this as sin X + sin Y. Surprisingly he was
correct. The values of X and Y differed by 10˚; what were these values,
Ans: Equal
assuming that 0˚ < X < Y < 360˚?
Ans: x = 175˚
Problem 103 y = 185˚
A pirate buried his treasure on an island, a conspicuous landmark of which
were three palm trees, each one 100 feet from the other two. Two of these
trees were in a N-S line. The directions for finding the treasure read: Problem 110
“Proceed from southernmost tree 15 feet due north, then 26 feet due west.” One side of the triangle is 10 feet longer than another and the angle between
Is the treasure buried within the triangle formed by the tree? them is 60˚. Two circles are drawn with these sides as diameters. One of the
points of intersection of the two circles is the common vertex. How far from
Ans: outside the triangle
the third side is the other point of intersection?
Ans: 0
Problem 104
An Origami expert started making a Nani-des-ka by folding the top left corner
of a sheet of paper until it touched the right edge and the crease passed Problem 112
through the bottom left corner. He then did the same with the lower right There is one flag at the entrance to a racetrack and another inside the track,
corner, thus making two slanting parallel lines. The paper was 25 inches long half a mile from the first. A jockey notes that no matter where he is on the
and the distance between the parallel lines was exactly 7/40 of the width. track, one flag is 3 times as far away as the other. How long is the track?
How wide was the sheet of paper?
Ans: 1980π
Ans: 24 inches
Problem 113
Problem 105 What is the longest 6’ wide shuffle board court which will fit in a 20’ x 30’
The Ben Azouli are camped at an oasis 45 miles west of Taqaba. They rectangular room?
decided to dynamite the Trans-Hadramaut railroad joining Taqaba to Ans: 30 7/8 ft.
Maqaba, 60 miles north of the oasis. If the Azouli can cover 18 miles a day,
how long will it take them to reach the railroad?
Problem 114
Ans: 2 days
Find the smallest number (x) of persons a boat may carry so that (n) married
couples may cross a river in such a way that no woman ever remains in the
Problem 106 company of any man unless her husband is present. Also find the least
number of passages (y) needed from one bank to the other. Assume that the
A yang, ying, and yung is constructed by dividing a diameter of a circle, AB,
boat can be rowed by one person only.
into three parts by points C and D, then describing on one side of AB
semicircles having AC and AD as diameters and on the other side of AB Ans: x = 2
semicircles having BD and BC as diameters. Which is larger, the central y=5
portion or one of the outside pieces?
Ans: Same
Problem 115
A, B and C participate in a track meet, consisting of at least three events. A
Problem 107 certain number of points are given for first place, a smaller number for
second place, and a still smaller number for third place. A won the meet with
A diaper is in the shape of a triangle with sides 24, 20 and 20 inches. The
a total score of 14 points; B and C are tied for second with 7 points apiece. B
long side is wrapped around the baby’s waist and overlapped two inches.
won first place in the high jump. Who won the pole vault assuming no ties
The third point is brought up to the center of the overlap and pinned in place.
occurred in any event?
The pin is to go through three thicknesses of material. What is the area in
which the pin may be placed? Ans: A
Ans: 2.5 in2
Problem 116
Maynard the Census Taker visited a house and was told, “Three people live
Problem 108 there. The product of their ages is 1296, and the sum of their ages is our
A hostess plans to serve a square cake with icing on top and sides. Upon house number.” After an hour of cogitation Maynard returned for more
determining how many guests want cake, what method should she use to information. The house owner said, “I forgot to tell you that my son and
insure that each guest will receive the same amount of cake and icing? grandson live here with me.” How old were the occupants and what was their
Ans: Top areas are equal to receive the same amount of cake. street number?
Side areas are equal to receive equal icing areas. Ans: age of occupants = 1 and 18, street number = 72
