Geometry/Notes 7.4
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This document discusses trigonometry and how it can be used to find unknown sides and angles of right triangles using trigonometric ratios like sine, cosine, and tangent. It provides examples of labeling sides and angles in a right triangle, calculating trig ratios for given angles, and using trigonometry to solve problems involving triangles and ladder heights at angles.
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The document discusses solving for unknown sides and angles of triangles using trigonometric functions like the law of sines. Several multi-step example problems are worked through that involve determining if a triangle is possible based on given information, finding missing side lengths, and calculating angles. Diagrams are included to illustrate each step of the example problems.
Triangles
This document is a project on triangles and their properties submitted to Florence Public School. It defines a triangle as a figure with three non-collinear points connected by three line segments. The six elements of a triangle are identified as the three sides and three angles. Various types of triangles are defined including equilateral, isosceles, scalene, acute, right, and obtuse triangles. Key properties of triangles discussed include the angle sum property, exterior angle property, triangle inequality property, and Pythagorean theorem. References used in creating the project are also listed.
Similar to Geometry/Notes 7.4 (11)
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Geometry/Notes 11.2
This document provides information on finding the areas of triangles, trapezoids, and rhombi. It gives the formulas for calculating the area of each shape, includes examples of applying the formulas, and provides practice problems for students to work through. The lesson plan is for a two-day unit covering adding the areas of different plane figures, with the first day focused on notes and examples, and the second day devoted to review and assessment.
Geometry/Notes 11.1
This document discusses finding the areas of parallelograms and using coordinate planes to identify parallelograms. It provides examples of calculating perimeters and areas of parallelograms. It also gives applications involving finding the area of yard spaces and floors. Students are asked to plot points on a coordinate plane to identify parallelograms and calculate their areas. The lesson plan is to introduce finding areas of parallelograms over two class periods with notes, examples, and a follow-up quiz.
Advanced/Notes 9.2
To solve static problems:
1. Make a free-body diagram showing all forces on each object.
2. Choose a coordinate system and resolve forces into components.
3. Write equilibrium equations for the sum of forces in each direction and the sum of torques.
4. Solve the equations to determine the unknown forces.
Advanced/Notes 9.1
The document discusses static equilibrium, which refers to when an object experiences forces but does not move or accelerate. It provides examples of a book sitting on a table and braces on teeth being in equilibrium, as the forces balance out. It also discusses calculating tensions in cords supporting a chandelier and the concept of levers providing mechanical advantage to allow smaller applied forces to move larger objects.
Geometry/Notes 10.6
This document discusses secants, tangents, and angle measures related to circles. It defines a secant as a line that intersects a circle at two points and presents three theorems relating the measures of angles formed by secants and tangents to the measures of the arcs they intercept. Examples demonstrate using the theorems to find measures of angles and arcs. The lesson plan is to take two days, with the first day covering notes and the second reviewing related material and giving a quiz.
Geometry/Notes 10.5
This document discusses tangents to circles and includes several theorems about tangents: a tangent intersects a circle at only one point and is perpendicular to the radius at that point; if a line is perpendicular to a radius it is tangent to the circle; and if two segments from the same exterior point are tangent to a circle they are congruent. Examples applying these theorems to find measures are provided. The document also defines a circumscribed polygon as one where every side is tangent to the enclosed circle. Homework problems from the textbook are assigned.
Geometry/Notes 10.4
This document discusses inscribed angles and theorems related to them. An inscribed angle is an angle whose vertex is on a circle and whose sides are chords of the circle. The intercepted arc is the arc created by the chords of the inscribed angle. Three theorems are presented: if two inscribed angles intercept congruent arcs, the angles are congruent; if an inscribed angle intercepts a semicircle, the angle is a right angle; and if a quadrilateral is inscribed in a circle, its opposite angles are supplementary. The lesson plan is to introduce inscribed angles and develop theorems about them over two class periods with notes, examples, and a quiz.
General/Notes 11.1
The document discusses the relationship between work and energy. It states that work causes a change in the energy of a system, transferring energy between the system and the external world. Energy can exist in different forms and be changed from one form to another. Examples are given of kinetic energy and gravitational potential energy, including the equation PE = mgh. Worksheets and practice problems are provided about calculating gravitational potential energy at different heights and the work done by gravity in lifting objects.
Geometry/Notes 10.3
This document covers geometry concepts related to arcs, chords, and theorems in circles. It discusses the relationship between arcs and chords, and theorem 10.3 which states that if a diameter or radius is perpendicular to a chord, it bisects the chord and its arc. The document provides examples and homework problems, and outlines a lesson plan to introduce rules about the relationship between chords and arcs over two class periods, including notes, examples, and a review quiz.
Goemetry/Notes 10.2
This document discusses angles and arcs in circles. It defines central angles as angles with the center of the circle as the vertex and radii as the sides. The measurement of an arc is equal to the measurement of its central angle. Arcs are classified as minor, semi-circle, or major depending on whether their central angle measures less than, equal to, or greater than 180 degrees, respectively. The document also provides examples of calculating arc measures and lengths using proportions relating the degree measure of the central angle to the arc length and circumference. There are homework problems assigned from the textbook.
Advanced/Notes 8.8
This document discusses angular momentum and its conservation. It provides an example of a mass attached to a string revolving in a circle on a table. Initially, the mass revolves at a radius r1 with a speed of v1 = 2.4 m/s. The string is pulled through a hole, reducing the radius to r2 = 0.48 m. The document asks the reader to calculate the new speed v2 based on the conservation of angular momentum. It also provides homework problems from page 222 problems 51-56 and 57-62 related to angular momentum and its conservation.
Advanced/Notes 8.7
This document discusses rotational kinetic energy and how to calculate it. It notes that both rotational and translational kinetic energy must be considered when using the law of conservation of energy. It provides an example of objects with the same potential energy at the top of an incline, but different times to reach the bottom based on their rotational inertia. Finally, it lists homework problems from page 221, numbers 43 through 48.
Geometry/Notes 10.1
This document provides information about circles and circumference. It defines a circle as all points equidistant from a center point and lists the parts of a circle as the center, radius, diameter, chord, and circumference. It gives examples of naming circle parts and using the circumference formula C=2πr to solve problems finding circumference given radius or diameter or to find radius or diameter given circumference. Students are assigned homework problems from their textbook on these concepts.
Advanced/Notes 8.5
This document discusses rotational dynamics and torque. It defines moment of inertia as relating to how mass is distributed about an axis of rotation. Greater moment of inertia means more mass is farther from the axis. Examples calculate moment of inertia for different axes of rotation for a system with two masses on a rod. Solving rotational dynamics problems involves drawing diagrams, identifying the system and forces, finding the axis of rotation, applying Newton's laws for rotation and translation, and checking units and magnitudes. The associated homework assignments problems 27-32 and 33-37, 42 are also listed.
Advanced/Notes 8.4
Torque is calculated based on the lever arm, which is the perpendicular distance from the axis of rotation to the point where a force is applied. A longer lever arm results in a greater torque. An example calculates the torque on a bicep muscle attached 5 cm from the elbow joint, based on different forces applied. A second example calculates the net torque on two connected wheels from two 50N forces, based on the wheels' radii serving as lever arms. The document concludes by assigning homework problems related to torque calculations.
Advnaced/Notes 8.2
This document discusses rotational motion and angular kinematics. It provides examples of calculating angular acceleration, revolutions, and angular velocity. Key equations for rotational motion are the same as linear motion but with angular quantities substituted. Examples include finding the angular acceleration and revolutions of a centrifuge rotor accelerating from rest to 20,000 rpm, and calculating values like angular velocity and revolutions for a slowing bicycle wheel. Readers are assigned homework problems applying these concepts.
Geometry/Notes 8.6
The document defines a trapezoid as a quadrilateral with one pair of parallel sides. It identifies the key terms used to describe trapezoids, including bases, legs, base angles, and medians. It provides an example problem involving verifying that a shape is a trapezoid and finding the endpoints of its median. Homework problems from the textbook are assigned.
Geometry/Notes 8.5
This document discusses properties of rhombi and squares. A rhombus is a quadrilateral with four congruent sides. A square is a rhombus and rectangle, with four equal sides and four right angles. Examples are provided to demonstrate determining whether shapes are rhombi, rectangles or squares based on given properties or vertex points. The homework assignments ask students to identify properties and classify shapes using given information.
General/Notes 10.1
This document discusses energy, work, and simple machines. It defines work as the product of the applied force and the distance moved in the direction of the force. It provides the work equation as W=Fd, where W is work, F is force, and d is distance. The document also discusses how work is related to changes in kinetic energy through the work-energy theorem. Examples are provided to demonstrate calculating work done by forces applied at an angle to the direction of motion and work done against gravity.
Advanced/Notes 8.1
This document provides an overview of rotational motion and angular quantities. It defines rotational motion as occurring when all points on an object move in circles around an axis of rotation. It reviews radians and their relationship to degrees, and provides an example problem calculating the angle an object subtends to a bird based on its visual capabilities. It also discusses angular kinematics, relating angular and linear velocity and acceleration, and examples of calculating velocities and accelerations for objects in rotational motion.
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Geometry/Notes 7.4
- 1. Trigonometry
- 2. • How can I find trigonometric ratios for right triangles?
- 3. • About triangle measurements • Uses ratios of sides of a triangle to describe an angle • Sine, Cosine and Tangent • Abbreviated as sin, cos and tan
- 4. • Which side is adjacent to angle B? • Which side is opposite to angle B? • Where is the hypotenuse? A c b C a B
- 5. • A c b C a B
- 6. • A c b C a B
- 7. • A c b C a B
- 8. •
- 9. • Find sin, cos, and tan for B B 13 5 C 12 A
- 10. • Find sin, cos and tan for A and B A 25 7 C 24 B
- 11. • Worksheet
- 12. • How can I use trigonometry to solve triangle problems?
- 13. • Calculator • (typically 4 places, round to the nearest ten-thousandth • sin 45 • cos 36 • tan 23
- 14. •
- 17. • A plane is one mile above sea level when it begins to climb at a constant angle of 3° for the next 60 ground miles. About how far above sea level is the plane after its climb?
- 18. • To guard against a fall, a ladder should make an angle of 75° or less with the ground. • A. What is the maximum height that a 20-foot ladder can reach safely? • B. How far from the building is the base of the ladder at maximum height?
- 19. • Worksheet