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Questions and Answers
What relationship do the ratios of sin x° and cos y° share?
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.
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).
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.
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?
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).
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).
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?
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?
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)?
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?
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?
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°?
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?
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?
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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