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Spherical Trigonometry
  • Prisil Mae Autentico

  • 問題数 20 • 8/28/2024

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    問題一覧

  • 1

    If Greenwich Mean Time (GMT) is 6 A.M., what is the time at a place located 30° East longitude?

    8 A.M.

  • 2

    If the longitude of Tokyo is 139°E and that of Manila is 121°E, what is the time difference between Tokyo and Manila?If the longitude of Tokyo is 139°E and that of Manila is 121°E, what is the time difference between Tokyo and Manila?

    1 hour and 12 minutes

  • 3

    One degree on the equator of the earth is equivalent to?

    4 minutes

  • 4

    A spherical triangle ABC as an angle C = 90° and sides a = 50º and c = 80°. Find the value of “b” in degrees.

    74.33°

  • 5

    Solve the remaining side of the spherical triangle whose given parts are A = B = 80° and a = b = 89°.

    168° 31’

  • 6

    Solve for the side b of a right spherical triangle ABC whose parts are a = 46°, c = 75° and C = 90°.

    68°

  • 7

    Given the right spherical triangle whose given parts are a = 82°, b = 62° and c = 90°. What is the value of the side opposite the right angle?

    86° 15’

  • 8

    Determine the value of the angle B of an isosceles spherical triangle ABC whose given parts are b = c = 54° 28’ and a = 92° 30’.

    41° 45’

  • 9

    Solve for angle A in the spherical triangle ABC, given a = 106º 25’, c = 42° 16’ and B = 114° 53’.

    97° 09’

  • 10

    Solve for angle C of the oblique triangle ABC given, a = 80°, c = 115° and A = 72º

    119°

  • 11

    Determine the spherical excess of the spherical triangle ABC given a = 56°, b = 65º and c = 78°.

    33° 33’

  • 12

    What is the spherical excess of a spherical triangle whose angles are all right angles?

    90°

  • 13

    The area of a spherical triangle ABC whose parts are A = 93º 40’, B = 64° 12’, C = 116º 51’ and the radius of the sphere is 100 m is?

    16531 sq. m.

  • 14

    A spherical triangle has an area of 327.25 sq. km. What is the radius of the sphere if its spherical excess is 30º?

    25 km

  • 15

    A ship on a certain day is at latitude 20º N and longitude 140º E. After sailing for 150 hours at a uniform speed along a great circle route, it reaches a point at latitude 10º S and longitude 170º W. If the radius of the earth is 3959 miles, find the speed in miles per hour.

    16.4

  • 16

    Calculate the area of a spherical triangle whose radius is 5 m and whose angles are 40°, 65°, and 110°.

    15.27 sq. m.

  • 17

    right spherical triangle has an angle C = 90°, a = 50°, and c = 80°. Find the side b.

    74.33°

  • 18

    If the time is 8:00 a.m. GMT, what is the time in the Philippines, which is located at 120° East longitude?

    4 p.m.

  • 19

    An airplane flew from Manila (14° 36’N, 121° 05’E) at a course of S 30° E maintaining a certain altitude and following a great circle path. If its groundspeed is 350 knots, after how many hours will it cross the equator?

    2.87 hours

  • 20

    Find the distance in nautical miles between Manila and San Francisco. Manila is located at 14° 36’N latitude and 121° 05’ E longitude. San Francisco is situated at 37° 48’ N latitude and 122° 24’ W longitude.

    6046.2 nautical miles