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    Prelims Solution Ce18

    Uploaded by

    Mark Lester Lualhati
    This document contains solutions to 15 problems involving geometry and trigonometry concepts such as: finding the velocity of wind given time traveled with and against the wind; calculating the time needed to fill a tank if the inlet and outlet pipes are open; and determining heights or distances using angles of elevation/depression and relationships between points. The solutions utilize principles of similar triangles, the angle sum of a triangle, properties of circles, and relationships between chords, arcs, segments and sectors.

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    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd

    Prelims Solution Ce18

    Uploaded by

    Mark Lester Lualhati
    235 views6 pages
    This document contains solutions to 15 problems involving geometry and trigonometry concepts such as: finding the velocity of wind given time traveled with and against the wind; calculating the time needed to fill a tank if the inlet and outlet pipes are open; and determining heights or distances using angles of elevation/depression and relationships between points. The solutions utilize principles of similar triangles, the angle sum of a triangle, properties of circles, and relationships between chords, arcs, segments and sectors.

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    This document contains solutions to 15 problems involving geometry and trigonometry concepts such as: finding the velocity of wind given time traveled with and against the wind; calculating the time needed to fill a tank if the inlet and outlet pipes are open; and determining heights or distances using angles of elevation/depression and relationships between points. The solutions utilize principles of similar triangles, the angle sum of a triangle, properties of circles, and relationships between chords, arcs, segments and sectors.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    235 views6 pages

    Prelims Solution Ce18

    Uploaded by

    Mark Lester Lualhati
    This document contains solutions to 15 problems involving geometry and trigonometry concepts such as: finding the velocity of wind given time traveled with and against the wind; calculating the time needed to fill a tank if the inlet and outlet pipes are open; and determining heights or distances using angles of elevation/depression and relationships between points. The solutions utilize principles of similar triangles, the angle sum of a triangle, properties of circles, and relationships between chords, arcs, segments and sectors.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
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    PRELIMINARY EXAMINATION SOLUTION – CE 18 – CORRELATION COURE1

    SOLUTION TO

    Problems:

    An airplane travels a distance of 500km against the wind in one hour and 45 minutes. Traveling
    the same distance with the wind, the airplane consumed one hour and 15 minutes. Find the
    velocity of the wind.

    A tank can be filled by an inlet pipe in 6 hours and can be emptied by an outlet in 12 hours. How
    much time needed to fill the tank if both the inlet and outlet pipe are open.

    A flagpole and a tower stands 36 meters apart on a horizontal plane. A person standing
    successively at their bases observes that the angle of elevation of the top of the tower is twice
    that of the pole, but at a point midway between their bases the angles of elevation are
    complementary. Find the height of the tower.

    PREPARED BY: ENGR. RUEL CATAPANG


    PRELIMINARY EXAMINATION SOLUTION – CE 18 – CORRELATION COURE1

    A 40-m high tower stands vertically on a hillside (sloping ground) which makes an angle of 18
    degrees with the horizontal. A tree also stands vertically up the hill from the tower. An observer
    on the top of the tower finds the angle of depression of the tree to be 28 degrees and the bottom
    of the tree to be 40 degrees. Determine the height of the tree.

    The top of the tower is sighted from point A and found to have an angle of elevation of 26
    degrees. When sighted at point B that is 300 m closer to the tower, the angle of elevation is 56
    degrees/ Points A and B are on the same horizontal plane with the base of the tower. What is
    the height of the tower?

    PREPARED BY: ENGR. RUEL CATAPANG


    PRELIMINARY EXAMINATION SOLUTION – CE 18 – CORRELATION COURE1

    Points A, B and C are in the horizontal circular plane where AB is the diameter equal to 24 m.
    The top of the pole standing at point A is sighted at B and C has angles of elevation equal to 20
    degrees and 30 degrees, respectively. Point C is along the circumference of the circle. Find the
    distance BC.

    The angle of elevation of the top of the vertical tower from points A and B are 25 degrees and
    50 degrees, respectively. The points A and B are 300 m apart and on the same horizontal plane
    with the foot of the tower. The horizontal angle subtended by A and B at the foot of the tower is
    90 degrees. Find the height of the tower.

    PREPARED BY: ENGR. RUEL CATAPANG


    PRELIMINARY EXAMINATION SOLUTION – CE 18 – CORRELATION COURE1

    Determine the area of a sector of a circle if its perimeter is 19 inches and radius is 6 inches.

    Two circles are tangent to a third circle internally and are tangent to each other externally. If the
    distances between their centers are 10 cm, 7 cm and 5 cm, respectively, compute the radius of
    the biggest circle.

    The length of common chord of two intersecting circles is 48 cm. The radius of one of the circles
    is 25 cm. If the distance between their centers is 39 cm, what is the diameter of the other circle?

    A sector of a circle of radius 4 feet has a central angle of 30 degrees. A line connecting one of
    the endpoints of the arc to the midpoint of the opposite edge is then drawn. Determin the are
    between the line, the arc and the edge adjacent to the drawn line and arc.

    PREPARED BY: ENGR. RUEL CATAPANG


    PRELIMINARY EXAMINATION SOLUTION – CE 18 – CORRELATION COURE1

    A quadrilateral ABCD is inscribed in a semi-circle with the side AD as its diameter. If point O is
    the center of the semi-circle, determine the angle DCO if angle CAD is 39 degrees.

    Two perpendicular chords both 5 cm the center of a circle divide the circle into four parts. if the
    radius of the circle is 13 cm. Compute the area of the smallest part.

    A square is inscribed in a semi-circle having a radius of 15 m. the base of the square is on the
    base diameter of the semi-circle. Find the area of an octagon inscribed in the square.

    PREPARED BY: ENGR. RUEL CATAPANG


    PRELIMINARY EXAMINATION SOLUTION – CE 18 – CORRELATION COURE1

    Find the area of quadrilateral ABCD inscribed in a circle where AB = 8 cm, BC = 15 cm, CD =
    12 cm and DA = 18 cm.

    PREPARED BY: ENGR. RUEL CATAPANG

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