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    Review MODULE: - MATHEMATICS (Trigonometry-Part 2)

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    YeddaMIlagan
    This document provides a review of topics in trigonometry including right triangles, oblique triangles, applications of trigonometry, spherical trigonometry, and miscellaneous problems. It includes formulas for solving problems involving sine, cosine, and other trigonometric functions applied to right triangles, oblique triangles, and spherical geometry. Several multi-part example problems are provided to demonstrate applications of trigonometric concepts.

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    Review MODULE: - MATHEMATICS (Trigonometry-Part 2)

    Uploaded by

    YeddaMIlagan
    256 views1 page
    This document provides a review of topics in trigonometry including right triangles, oblique triangles, applications of trigonometry, spherical trigonometry, and miscellaneous problems. It includes formulas for solving problems involving sine, cosine, and other trigonometric functions applied to right triangles, oblique triangles, and spherical geometry. Several multi-part example problems are provided to demonstrate applications of trigonometric concepts.

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    Review-Module-3-Trigonometry-Part-2

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    This document provides a review of topics in trigonometry including right triangles, oblique triangles, applications of trigonometry, spherical trigonometry, and miscellaneous problems. It includes formulas for solving problems involving sine, cosine, and other trigonometric functions applied to right triangles, oblique triangles, and spherical geometry. Several multi-part example problems are provided to demonstrate applications of trigonometric concepts.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    256 views1 page

    Review MODULE: - MATHEMATICS (Trigonometry-Part 2)

    Uploaded by

    YeddaMIlagan
    This document provides a review of topics in trigonometry including right triangles, oblique triangles, applications of trigonometry, spherical trigonometry, and miscellaneous problems. It includes formulas for solving problems involving sine, cosine, and other trigonometric functions applied to right triangles, oblique triangles, and spherical geometry. Several multi-part example problems are provided to demonstrate applications of trigonometric concepts.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 1

    MANILA: Room 206, JPD Building, CM Recto Avenue, Manila

    CEBU: 4/F J. Martinez Bldg., Osmeña Blvd., Cebu City


    Telephone Number: (02) 516-7559 (Manila) E-Mail: buksmarquez1 @yahoo.com
    (032) 254-9967 (Cebu)

    Review MODULE – MATHEMATICS (Trigonometry- Part 2)

    APPLICATIONS OF PLANE TRIGONOMETRY SPHERICAL TRIGONOMETRY


    RIGHT TRIANGLE SINE LAW
    (PYTHAGOREAN TRIANGLE) sin a sin b sin c
    = =
    r 2 = x 2 + y2 sin A sin B sin C
    x = r cos θ
    COSINE LAW FOR ANGLES
    y = r sin θ
    cos A = − cos B cos C + sin B sin C cos a
    OBLIQUE TRIANGLES cos B = − cos A cos C + sin A sin C cos b
    (NO RIGHT ANGLE) cos C = − cos A cos B + sin A sin B cos c
    SINE LAW COSINE LAW FOR SIDES
    a b c
    = = cos a = cos b cos c + sin b sin c cos A
    sin A sin B sin C
    cos b = cos a cos c + sin a sin c cos B
    COSINE LAW cos c = cos a cos b + sin a sin b cos C
    a2 = b2 + c 2 − 2bc cos A
    AREA OF SPHERICAL TRIANGLE SPHERICAL EXCESS
    b2 = a2 + c 2 − 2ac cos B
    πR2 E
    c 2 = a2 + b2 − 2ab cos C A= E = A + B + C − 180
    180
    1. Two people are a meter apart and the height of one is double that VOLUME OF A SPHERICAL PYRAMID
    of the other. If from the middle point of the line joining their feet, π R3 E
    an observer finds the angular elevation of their tops to be V = 1⁄3 Ah =
    540°
    complementary, find the height of the taller person (in terms of a) 1 Nautical mile = 6080 feet
    in meters.
    1 Statute mile = 5280 feet
    2. P is a point on BC of the triangle ABC such that AB = AC = BP. If 1 min (0°01’00”) = 1 Nautical mile
    PA = PC, find the value of the angle ABC.
    12. Given the parts in a spherical triangle b=34°, c=58° and C= 90°,
    3. Towers A and B are constructed on a horizontal plane, B being determine the all the parts of the spherical triangle.
    200 m. above the plane. The angle of elevation of the top of Tower
    A as seen from point C in the plane (in the same vertical plane SITUATION.
    with A and B) is 50˚, while the angle of depression of C viewed Given the parts in a spherical triangle A=120°, B=135°, and C = 80°. R
    from the top of Tower B is 28˚ and the angle subtended at the top = 1,000 km
    of Tower B by the top of Tower A and C is 50˚, find the height of 13. Determine the terrestrial angle ‘a’.
    A. 14. Determine the length of arc BC.
    15. Determine the area of the spherical triangle.
    4. The angle of elevation of the tower from A is 25 degrees. From
    another point B, the angle of elevation of the top of the tower is 16. Northwest Airlines planes flying from Chicago to Manila (14.6° N,
    56°. if the distance between A and B is 300 m and on the same 121.0° E) have to land first at Narita Airport in Tokyo (35.7° N,
    horizontal plane as the foot of the tower. The horizontal angle 139.7° E) before proceeding to Manila. If the trip from Tokyo to
    subtended by A and B at the foot of the tower is 70°. What is the Manila takes 4.5 hours, what is the speed of the plane? What is
    height of the tower? the course of the plane from Tokyo?

    5. Points D and E are the midpoints of the sides BC and CA,


    respectively, in triangle ABC. If AD=5 and BC=BE=4, find the
    length of CA.

    6. Airplanes A and B are flying with constant speed in the same


    vertical plane at angles 30 degrees and 60 degrees with respect
    to the horizontal, respectively. The airspeed of A is 100 sqrt 3
    meters per second. Initially, an observer in A sees B directly ahead
    at the same altitude at a (horizontal) distance of 500m. Assuming
    they take no evasive action and collide, after how many seconds
    does this happen?

    7. Given isosceles trapezoid ABCD with AB=CD, and the acute


    angles B and C satisfy sin B = 4/9 and sin C=5/6, determine the
    ratio of the area of triangle ABC to area of triangle BDC.

    MISCELLANEOUS PROBLEMS
    SITUATION
    Given triangle ABC, how many possible triangles can be formed for the
    following conditions:
    8. BC = 15cm, AC = 7cm, AB = 8cm.
    9. BC = 17cm, AC = 12cm, AB = 7cm.
    10. BC = 16cm, AC = 26cm, angle A = 42.3°.
    11. AB = 37cm, AC = 26cm, angle B = 32.5°.

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