Friday, June 21, 2024

# Geometry Marking Diagrams Worksheet Answers

## Dynamically Created Math Worksheets

KutaSoftware: Geometry- Information In Geometric Diagrams Part 2

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The website contains over 94 different math topics with over 1223 unique worksheets.These math worksheets are a great resource for Kindergarten through 12th grade.They may be customized to fit your needs and may be printed immediately or saved for later use. These math worksheets are randomly created by our math worksheet generators, so you have an endless supply of quality math worksheets at your disposal. These high quality math worksheets are delivered in a PDF format and includes the answer keys. Our math worksheets are free to download, easy to use, and very flexible. A detailed description is provided in each math worksheets section.

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## Independent And Dependent Events

We need to understand independent and dependent events to be able to do the next sections.

• Two or more events are independent if one event doesnt effect the probability of the others happening.
• Two or more events are dependent if one event does effect the probability of the others happening.

Example:

• Getting a head both times on 2 coin flips are independent events.
• Picking a red marble at random from a bag, then picking a green marble without replacing the red marble are dependent events.
• The AND rule states that: If two events, A and B, are independent, then,

\text = \text \times \text

This means to find the probability of A and B occurring you must multiply the probability of A occurring by the probability of B occurring.

## Example : Drawing A Bearing More Than 180

Draw a bearing of 300^

Locate the point you are measuring the bearing from and draw a north line if there is not already one given.

Using your protractor, place the zero of the scale on the north line and measure the required angle clockwise, make a mark on your page at the angle needed.

If you have a 180^ protractor, we need to subtract the bearing required from 360^

360^ – 300^ = 60^ , so measure 60^ anticlockwise

Draw a line from the start point in the direction of the bearing. If you are producing a scale drawing and know the distance to locate a point use this scale appropriately.

## Example : Calculating A Back Bearing

The bearing of B from A is 070^ . Calculate the bearing of A from B.

Locate the points you are calculating the bearing from and to.

Using the north lines for reference at both points, use angle rules and/or trigonometry to calculate any angles that are required.

Drawing a north line at B and extending the line from A to B shows us a corresponding angle. If we travel from A to B, we need to turn another 180^ to return back to A. 180^ + 70^ = 250^

Read off the three-figure bearing required.

The bearing of A from B is 250^ .

## Free Body Diagrams Worksheet Answer Key

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Free Body Diagrams Worksheet

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## Example : Calculate A Bearing Using Sohcahtoa

A ship sails 7 km due east from a point P to point A. It then sails 3 km due south from A to point B. Calculate the bearing of B from P.

Locate the points you are calculating the bearing from and to.

Sketch the diagram to help visualise the problem.

Using the north lines for reference at both points, use angle rules and/or trigonometry to calculate any angles that are required.

Drawing a line from P to B forms a right angled triangle. Use trigonometry to find the angle APB. Then add this to 90^ .

^}\left=23^ to the nearest degree

90^ +23^\circ =113^

Read off the three-figure bearing required.

The bearing of B from P is 113^ .

## Worksheet On Math Relation

Students can practice various questions from Relation to get grip on the concepts. This Worksheet on Math Relation covers various topics like Mapping for Relations, Representing Relations using a set of ordered pairs, arrow diagrams, etc. Solve the Ample Problems provided in the Math Relation Worksheet and get a better idea of the concepts within it. Practice the problems on your own and cross-check your solutions with the step by step solutions provided to understand where you went wrong.

1. If A= , B = . What is the number of elements in AxB?

Solution:

2. Determine the domain and range of the given function

Range =_____

Solution:

Given Function is

Domain is the first component of the ordered pairs and second component in the ordered pairs is the Range.

Domain =

Range =

3. Represent Relation using an Arrow Diagram?

Solution:

Take the Domain Values on the left column and Range Values in the Right Column and mark the relation between them using arrows.

4. Let A = B = be two sets and let R be a relation from A to B is multiple of. Represent in the Set of Ordered Pairs?

Solution:

5. Given the relation R = . Which of the following values for x will make relation R a function? 8

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## Example : Drawing A Scale Drawing With A Bearing

Make a scale drawing of a point Q 8 km away from a point P on a bearing of 110^ from P, using a scale of 1 cm : 2 km.

Locate the point you are measuring the bearing from and draw a north line if there is not already one given.

Using your protractor, place the zero of the scale on the north line and measure the required angle clockwise, make a mark on your page at the angle needed.

If the angle is more than 180^ and you do not have a full circle protractor then you should subtract the required angle from 360^ , and then measure this angle anticlockwise from the north line.

Draw a line from the start point in the direction of the bearing. If you are producing a scale drawing and know the distance to locate a point use this scale appropriately.

If the scale is 1cm : 2km , we will need to measure 4 cm to locate Q.

## Example : Calculating A Bearing Around A Point

KutaSoftware: Geometry- Information In Geometric Diagrams Part 1

Calculate the bearing of A from P.

Locate the points you are calculating the bearing from and to.

Using the north lines for reference at both points, use angle rules and/or trigonometry to calculate any angles that are required.

We need the angle around the point P clockwise from the north line. We know that angles on a straight line add to 180^. 180^ + 53^ = 233^

Read off the three-figure bearing required.

The bearing of A from P is 233^ .

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## Example : Drawing A Bearing Less Than 180

Draw a bearing of 050^

• Locate the point you are measuring the bearing from and draw a north line if there is not already one given.
• 2Using your protractor, place the zero of the scale on the north line and measure the required angle clockwise, make a mark on your page at the angle needed.

3Draw a line from the start point in the direction of the bearing. If you are producing a scale drawing and know the distance to locate a point use this scale appropriately.

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## How To Draw Bearings

In order to draw bearings:

• Locate the point you are measuring the bearing from and draw a north line if there is not already one given.
• Using your protractor, place the zero of the scale on the north line and measure the required angle clockwise, make a mark on your page at the angle needed.
• Draw a line from the start point in the direction of the bearing. If you are producing a scale drawing and know the distance to locate a point use this scale appropriately.
• ## What Are Bearings

Bearings are angles, measured clockwise from north.

To measure a bearing, we must first know which direction is north.

This north direction is usually provided in the maths exam question. We then measure the required angle in a clockwise direction. All bearings need to be given in three figures, so if the angle measured is less than 100 degrees, we must start the three-figure bearing with a zero.

Example:

The diagram shows three points A, B and P.

The angles are measured clockwise from the north line.

The bearing of A from P is 045^ .

The bearing of B from P is 260^ .

Bearings are used by sailors and pilots to describe the direction they are travelling. They are also used on land by hikers and the military.