01-SURVEYING METHEMATICS Flashcards
- A surveyor receives a request from a client on a control project to report the results in state plane coordinates, expressed in meters. The project is in a state that has adopted the U.S. survey foot as its standard. In such a state, which relationship is
correct’?
(A) 1 ft = 0.3048006 m
(B) 1 m = 3.2808000 ft
(C) 1 m = 3.2808399 ft
(D) 1 ft = 0.3048000 M
(A) 1ft = 0.3048006
Solution: The key to this question is the adoption of the survey foot rather than the international foot. Some states have adopted the international foot, which is defined by the wavelength of light emitted when krypton gas is electrically excited. Answers (C) and (D) are correct relationships for describing the international foot.
1 m = 39.37 U.S. in
1 ft = 12 in
1 U.S. Survey Foot = 12in/(39.37 in/m) = 0.3048006m
- A surveyor making measurements to guide a welder in the installation of a sill on a building wall must provide a 1.40-ft minimum clearance along this property line. However, the welder requires the measurement in feet and inches. What is 1.40-ft expressed to the nearest eight of an inch?
(A) 1ft, 4-3/8in
(B) 1ft, 3-5/8in
(C) 1ft, 4-3/4in
(D) 1ft, 3-1/8in
(C) 1ft, 4-3/4in
Solution: The number of whole feet remains the same (1 ft). To convert 0.40 ft into inches, use a proportion.
40/100 = X/12in
X = (12in)*(40/100)
X = 4.8in
Since the answer must be in eights of an inch, the next step is to convert 8/10 of an inch into eights of an inch.
8/10 =x/8
X = (8)*(8/10)
X = 6.4
6.4/8 = 3.2/4in (round to 3/4 inches)
- A surveyor staking a circular arc 100 ft long finds that the plans show the curve has a degree
of curve of one. The surveyor is about to calculate the length of the radius when the party chief
says, “It is simply 100 times 1 radian.” Which of the following relationships correctly describes 1 radian?
(A) 1 radian = pi/360°
(B) 1 radian = 180°/pi
(C) 1 radian = 57°29’58”
(D) 1 radian = pi/3200 mils
(B) 1 radian = 180°/pi
Solution:
A radian is the angle at the center of a circle subtended by an arc with a length equal to the circle’s radius. The radian is a unit convenient in calculating circular curves that are expressed in degrees of curve. One radian is equal to 180° /pi, or 57° 17’ 44.8”
- A property owner from overseas writes to his surveyor with instructions concerning a
survey. One of the instructions says, “Please be certain that the property has at least 4
hectares.” What is a hectare?
(A) a large shade tree with gray bark
(B) a type of concrete n10nurnent
(C) a category of easements
(D) a measure of area.
(D) A measure of area
Solution: A hectare is a measure of land area in the metric system. The term is built on the word are, which is 100 square meters, with the prefix hect, which indicates multiplication by 100. Therefore, a hectacre is equal to 10,000 square meters, or 2.471 acres.
- Which numerical value is equal to (S1t·¾7
(A) 5.84
(B) 3
(C) -3
(D) 1/3
(D) 1/3
Solution: The expression (81)^(-1/4) may be expressed as the inverse of the fourth root of 81.
- While shopping for an inexpensive theodolite, a surveyor finds that the instrument with the lowest price has a circle that is divided into more graduations than usual. The merchant explains that it is a European instrument and the circle is divided into grads. Which relationship correctly describes a grad?
(A) 1 grad = 00 °54’
(B) 1.5 grads = 01°
(C) 01° = 0.9 grads
(D) 10° = 100 grads
(A) 1 grad = 00°54’
Solution: A grad, also known as grade, is one hundredth of a right angle. There are 400 grads in a circle₁ so the grad is a smaller increment than a degree. The degree is a unit of the sexagesimal system and the grad is a unit of the centesima system. One grad is 0.9 of a degree, or 00°54’.
7.An old deed describes two corner monuments as being 18 rods apart. The monuments are recovered and found to be 300 ft apart. What is the difference between the two measurements?
(A) 1 yard
(B) 0.25 rod
(C) 1 meter
(D) 2 feet
(A) 1 yard
Solution: Early surveyors used a rod, otherwise know as a pole or a perch whose length was approximately 16-1/2ft. While these units are now considered archaic, they are still found in the public record. Eighteen rods is equivalent to 297 ft. If the current measurement is 300 ft, the difference is 3 ft, or 1 yd.
- While preparing to set the parts per million on an EDM, the surveyor discovers that the only chart available is calibrated in degrees Celsius. The thermometer indicates 68° Fahrenheit. What is the corresponding temperature in degrees Celsius?
(A) 90° C
(B) 6° C
(C) 55.5° C
(D) 20° C
(D) 20° C
Solution: According to the Celsius (or Centigrade) temperature scale, water freezes at 0° and boils at 100°. The corresponding freezing and boiling points on the Fahrenheit scale are 32° and 212°, respectively. The conversion from one to the other can he expressed as
°F = (9/5)°C+32°
°C = (5/9)*(°F-32°)
To find 68°F in degrees Celsius,
°C = (5/9)(68°-32°)
°C = (5/9)(36°)
°C = 20°
- While working down a section line from a witness a corner monument toward a standard corner in the public land survey system, a surveyor finds that the record length indicates a measurement of 15 chains, 64 links. Which value corresponds to that length?
(A) 514ft, 3in
(B) 313.05 meters
(C) 64.52 rods
(D) 344.08 yards
(D) 344.08 yards
Solution: In the PLSS, the unit defined by Gunter’s chain remains the standard, even thought the instrument is long out of use. The chain is 66ft long and is divided into 100 links. Therefore, the measurement can be expressed as
15 chains, 64 links = 15.64 chains
(15.64 chains)*(66ft/1chain) = 1032.24 feet)
(1032.24 feet)(1yard/3feet) = 344.08 yards
- What is the sum of the following fractions of an inch?
1/4in, 1/16in, 17/32in, 5/8in, 1/32in
(A) 1-3/4in
(B) 6/16in
(C) 1in
(D) 1-1/2in
(D) 1-1/2in
(8/32)+(2/32)+(17/32)+(20/32)+(1/32) = 1-16/32 = 1-1/2
- In the Cartesian coordinate system, the cosine and secant functions are positive in two of the four quadrants. In which two quadrants does this occur?
A. 1st and 2nd
B. 3rd and 4th
C. 1st and 4th
D. 2nd and 3rd
C. 1st and 4th
Solution: All trig functions are positive in the first quadrant. In the second quadrant, all are negative except two: the tangent and cotangent. In the fourth quadrant, the cosine and secant functions are positive, and all others are negative.
- In an equilateral triangle, what is the sine of half of any one of the interior angles?
A. 0.866
B. 1.000
C. 0.707
D. 0.500
D. 0.500
Solution: In an equilateral triangle, all interior angles are equal. Since the angles must equal 180°, or 60° per angle. The Sine of 30° is 0.500.
LC=2R*sin(I/2)
Formula for Long Chord
