Questions and Answers
What relationship do the ratios of sin x° and cos y° share?
Write an equation of a line that passes through the point (8, 4) and is parallel to the line y = 4x + 2.
Calculate the area of triangle ABC with altitude CD, given A (6, 0), B (1, 5), C (2, 0), and D (4, 2).
Find B, where segment with endpoints A (3, 4) and C (5, 11) is partitioned by point B such that AB and BC form a 2:3 ratio.
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What is the distance, CD, between the boats traveling along directions AC and AD?
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Find the perimeter of a quadrilateral with vertices at C (−2, 4), D (−3, 1), E (1, 0), and F (−1, 2).
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If point M is the midpoint of segment AB and A is located at (2, 6), find the location of point B if M is at (−1, 8).
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What is the height, in feet, of the portion AB of the lamppost bent at point A after a storm?
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How can Sammy use coordinate geometry to determine whether quadrilateral EFGH is a parallelogram?
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Which of the following is the equation of Leo's line that is perpendicular to a given line and passes through point (F, G)?
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What is the distance, in feet, that the box has to travel to move from point A to point C?
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Which of the following could be used to calculate the coordinates for point B, given that segment AB has point A located at (8, 9) and the distance from A to B is 10 units?
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Which pair of angles has congruent values for the sin x° and the cos y°?
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What is the length of the portion BC of the cloth?
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What is the length of the wood that is needed to replace AD in the triangular wooden frame ABC?
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Study Notes
Ratios and Relationships
- Ratios of sin x° and cos y° can be identical, as shown by the example 12 / 13 and 12 / 13.
- Recognizing that certain ratios can be reciprocals or negative is essential in understanding trigonometric relationships.
Linear Equations
- The equation of a line parallel to y = 4x + 2 passing through (8, 4) is y = 4x - 28.
Area of Triangles
- The area of triangle ABC, defined by points A (6, 0), B (1, 5), C (2, 0), and altitude CD, is determined to be 10 square units.
Segment Partitioning
- Point B, which partitions the segment with endpoints A (3, 4) and C (5, 11) in a 2:3 ratio, is located at (3.8, 6.8).
Distance Calculation
- The distance between two boats, traveling from point A along different directions, measured as CD, is 115.5 ft.
Perimeter of a Quadrilateral
- The perimeter of a quadrilateral with vertices C (−2, 4), D (−3, 1), E (1, 0), and F (−1, 2) calculates to approximately 12.35 units.
Midpoint and Coordinates
- Point B can be found at (−4, 10) if point M (−1, 8) is the midpoint between A (2, 6) and B.
Geometry and Trigonometry
- The height of the portion AB of a bent lamppost is given by the calculation 20 tan 55°.
Identifying Parallelograms
- To determine if quadrilateral EFGH is a parallelogram, use the slope formula to show that the opposite sides have equal slopes based on coordinates.
Perpendicular Lines
- The equation of the line that is perpendicular to a given line and passes through point (F, G) is stated as y - G = -2(x - F).
Distance along a Ramp
- The distance that a box moves from point A to C while sliding down a ramp is expressed as 14 cosec 68°.
Coordinate Calculation
- To find the coordinates for point B, use the equation: 10 = square root of the quantity of (x - 8)² + (y - 9)².
Congruent Angles
- Pairs of angles with congruent values for sin x° and cos y° are exemplified by angles 35° and 55°.
Lengths in Triangles
- The length of portion BC in a triangular piece of cloth can be calculated with 6 sin 32°.
Replacement of Wood
- The required length of wood to replace side AD in the triangular wooden frame ABC is measured at 5.1 inches.
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