Level 5 NZ Curriculum Achievement Objectives for Trigonometry
In a range of meaningful contexts, students will be engaged in thinking mathematically and statistically. They will solve problems and model situations that require them to:
GM5-10: Apply trigonometric ratios and Pythagoras’ theorem in two dimensions.
GM5-10: Apply trigonometric ratios and Pythagoras’ theorem in two dimensions.
In this unit you will revise:
1) Pythagorean Theorem (finding the hypotenuse) |
In this unit you will learn:
2) Pythagorean Theorem (finding any side) 3) The three trigonometric ratios 4) Use trigonometric ratios to find a side 5) Use trigonometric ratios to find an angle 6) Similar Triangles |
1) Pythagorean Theorem (finding the hypotenuse)
geometry._level_7._pythagoras._the_hypotenuse._answers.pdf | |
File Size: | 240 kb |
File Type: |
2) Pythagorean Theorem (finding any side)
We use the same formula to find any side of a right angled triangle. Always remember that c must be labelled as the longest side. Fill the numbers in the formula and then rearrange to find the answer.
|
|
geometry._level_7._pythagoras._missing_lengths._answers.pdf | |
File Size: | 296 kb |
File Type: |
geometry._level_7._pythagoras._pythagoras_word_problems._answers.pdf | |
File Size: | 315 kb |
File Type: |
TrigonometryA) Labeling triangles
Just like with Pythagorean Theorem, the longest side is called the HYPOTENUSE. The other two sides are labelled according to which angle is being used. The side that is opposite the angle is labelled as OPPOSITE. The side that is attached to the angle is called the ADJACENT. |
B) The trigonometric Ratios
Triangles that have the same angles but different sides are called SIMILAR TRIANGLES. Each angle has a specific ratio that uses the sides.
Triangles that have the same angles but different sides are called SIMILAR TRIANGLES. Each angle has a specific ratio that uses the sides.
4) Use Trigonometric Ratios to find a side
Use the following steps to find the side of a right angled triangle:
1) Circle the angle that has been given (not the right angle)
2) Label the sides correctly with HYPOTENUSE, OPPOSITE and ADJACENT (only two of the sides will have numbers)
3) Use SOH CAH TOA to find out which trigonometric ratio to use
4) Fill in the trigonometric equation:
- if the unknown is in the numerator, multiply by the denominator
- if the unknown is in the denominator, divide by the numerator
1) Circle the angle that has been given (not the right angle)
2) Label the sides correctly with HYPOTENUSE, OPPOSITE and ADJACENT (only two of the sides will have numbers)
3) Use SOH CAH TOA to find out which trigonometric ratio to use
4) Fill in the trigonometric equation:
- if the unknown is in the numerator, multiply by the denominator
- if the unknown is in the denominator, divide by the numerator
geometry._level_8._trigonometry._trigonometry__a__missing_lengths._answers.pdf | |
File Size: | 289 kb |
File Type: |
5) Use Trigonometric Ratios to find an angle
Use the following steps to find the angle of a right angled triangle:
1) Circle the angle that has been given (not the right angle) 2) Label the sides correctly with HYPOTENUSE, OPPOSITE and ADJACENT (only two of the sides will have numbers) 3) Use SOH CAH TOA to find out which trigonometric ratio to use 4) Fill in the trigonometric equation 5) Use must use the INVERSE TRIG RATIOS to find an angle. This means using your calculator a bit different. |
geometry._level_8._trigonometry._trigonometry__b__missing_angles_and_lengths._answers.pdf | |
File Size: | 261 kb |
File Type: |
6) Similar Triangles
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion . In other words,similar triangles are the same shape, but not necessarily the same size. The triangles are congruent if, in addition to this, their corresponding sides are of equal length
|
We can use the ratios to help us find the side of a triangle.
geometry._level_8._similarity_and_congruence._similar_triangles__a_._answers.pdf | |
File Size: | 293 kb |
File Type: |
Check out these websites for more help on trigonometry and similar triangles:
https://www.mathsisfun.com/algebra/trigonometry.html
http://serc.carleton.edu/mathyouneed/trigonometry/index.html
http://www.onlinemathlearning.com/trigonometry-games.html
https://www.mathsisfun.com/geometry/triangles-similar.html
https://www.mathsisfun.com/algebra/trigonometry.html
http://serc.carleton.edu/mathyouneed/trigonometry/index.html
http://www.onlinemathlearning.com/trigonometry-games.html
https://www.mathsisfun.com/geometry/triangles-similar.html