Trigonometry, finding angles and lengths in right angled triangles

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From users who are members of EUN257 Post-class activities :

Bennett Gardiner

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Ready to use

5 years, 8 months ago

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Bennett Gardiner 5 years, 8 months ago

Gave some feedback: Ready to use

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Bennett Gardiner 5 years, 11 months ago

Created this as a copy of Trigonometry: Right angled: Find approx side lengths.

Name	Status	Author	Last Modified
Trigonometry: Right angled: Finding trig ratios	Ready to use	Ben Brawn	17/10/2023 01:13
Trigonometry: Right angled: Finding reciprocal trig ratios	Ready to use	Ben Brawn	17/10/2023 01:13
Pythagoras' Theorem: Integers	Ready to use	Ben Brawn	25/09/2024 05:36
Trigonometry: Right angled: Find exact angles	Ready to use	Ben Brawn	16/02/2023 00:20
Trigonometry: Right angled: Find angles to nearest degree	Ready to use	Ben Brawn	04/04/2023 00:35
Trigonometry: Right angled: Find approx side lengths	Ready to use	Ben Brawn	04/04/2023 00:35
Trigonometry and vectors: Find angles to nearest degree	Ready to use	Ben Brawn	03/11/2021 12:47
Trigonometry and vectors: Find approx lengths of components	Ready to use	Ben Brawn	16/06/2016 07:00
Don's copy of Trigonometry: Right angled: Find exact angles	Ready to use	Don Shearman	01/06/2016 09:47
Trigonometry: Right angled: Finding trig ratios	draft	steve kilgallon	02/08/2016 15:02
trigo de triangulo	draft	Marlon Arcila	19/09/2016 16:44
rigonometry: Right angled: Finding trig ratios	draft	Marlon Arcila	31/08/2016 17:48
Solucion triangulos rectangulos angulos	draft	Marlon Arcila	19/09/2016 16:50
Trigonometry: Right angled: Finding trig ratios	draft	Paul Howes	14/11/2016 18:07
Pythagoras' Theorem: Integers	draft	Paul Howes	14/11/2016 18:07
Hannah's copy of Trigonometry and vectors: Find approx lengths of components	draft	Hannah Bartholomew	18/09/2017 16:14
Hannah's copy of Pythagoras' Theorem: Integers	draft	Hannah Bartholomew	18/09/2017 16:04
Trigonometry: Right angled: Finding trig ratios	draft	Paul Hancock	28/08/2017 02:29
Question 1	draft	Paul Hancock	05/09/2017 03:55
Question 3	draft	Paul Hancock	05/09/2017 03:39
Question 2	draft	Paul Hancock	05/09/2017 03:39
MATH6058 Trigonometry: Right angled: Finding trig ratios	draft	Catherine Palmer	24/10/2017 11:04
MATH6058 Trigonometry: Right angled: Find angles to nearest degree	draft	Catherine Palmer	23/10/2017 00:54
Trigonometry: Right angled: Finding trig ratios	draft	Mark Hodds	16/03/2018 09:52
Trigonometry: Right angled: Find angles to nearest degree	draft	Mark Hodds	16/03/2018 09:52
Samantha's copy of Trigonometry: Right angled: Finding trig ratios	draft	Samantha Konig	28/06/2018 01:10
Samantha's copy of Samantha's copy of Trigonometry: Right angled: Finding trig ratios	draft	Samantha Konig	28/06/2018 01:10
Trigonometry: Right angled: Finding trig ratios	draft	Paul Emanuel	28/06/2018 01:20
Trigonometry: Right angled: Find angle to nearest degree	draft	Clare Lundon	30/10/2018 21:41
Trigonometry: Right angled: Find angle to nearest degree	Has some problems	Clare Lundon	30/10/2018 21:52
Terry's copy of Trigonometry: Right angled: Find approx side lengths	draft	Terry Young	03/04/2019 17:51
Terry's copy of Trigonometry: Right angled: Finding trig ratios	draft	Terry Young	03/04/2019 17:54
Terry's copy of Trigonometry: Right angled: Find angles to nearest degree	draft	Terry Young	03/04/2019 17:54
Trigonometry, finding angles and lengths in right angled triangles	Ready to use	Bennett Gardiner	26/07/2019 12:42
Kapittel 1	draft	Arnhild Lunde	03/05/2019 10:52
Meetu's copy of Terry's copy of Trigonometry: Right angled: Find angles to nearest degree	draft	Meetu Chhabra	21/05/2019 05:13
Maria's copy of Trigonometry and vectors: Find approx lengths of components	draft	Maria Aneiros	24/05/2019 00:48
Maria's copy of Trigonometry and vectors: Find angles to nearest degree	draft	Maria Aneiros	24/05/2019 00:48
Maria's copy of Trigonometry: Right angled: Finding trig ratios	draft	Maria Aneiros	29/05/2019 08:38
Trigonometry: Right angled: Finding trig ratios	draft	Xiaodan Leng	11/07/2019 05:51
Trigonometry and vectors: Find angles to nearest degree	draft	Xiaodan Leng	11/07/2019 05:51
Trigonometry and vectors: Find approx lengths of components	draft	Xiaodan Leng	11/07/2019 05:52
Trigonometry: Right angled: Find angles to nearest degree	draft	Xiaodan Leng	11/07/2019 05:53
Trigonometry: Right angled: Finding reciprocal trig ratios	draft	Xiaodan Leng	11/07/2019 05:54
Trigonometry: Right angled: Find exact angles	draft	Xiaodan Leng	11/07/2019 05:55
Right Angled Trigonometry: Find angles to nearest degree	draft	Michael Proudman	07/12/2021 10:48
Right Angle Trigonometry (missing angle)	Ready to use	Andrew Chuter	06/04/2020 13:31
Cameron's copy of Right Angle Trigonometry (missing angle)	draft	Cameron Ritchie	10/07/2020 03:18
Trigonometry: Right angled: Find angles to nearest degree (JSXGraph through JME version)	draft	Christian Lawson-Perfect	07/12/2021 13:45
Trigonometry: Right angled: Find angles to nearest degree (Eukleides version)	draft	Christian Lawson-Perfect	07/12/2021 14:08

There are 80 other versions that do you not have access to.

Question statement

In a right angled triangle, we can use the trigonometric functions to obtain the values of unknown lengths and angles. For example, in the triangle below, $\ \sin(\theta) = \displaystyle \frac{b}{c}, \$ $\cos(\theta) = \displaystyle \frac{a}{c}, \$ $\tan(\theta) = \displaystyle \frac{b}{a}.$

The area of a triangle is its base times its height, so $A = \displaystyle\frac{1}{2}ab$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

triples	list	[ 407, 624, 745 ]
vec1	list	[ 0, 1, 2 ]
v	string
h	integer	624
d	string	$x$
scale	rational	1/26
tritop	decimal	dec("7.8269")
deltax	decimal	dec("-8.9337")
switcharoo	integer	1
smallest_angle	number	33.11
complement	number	56.89
anglelist	list	[ 33.11, 3, "$\\theta$" ]
display_angles	list	[ 33.11, "" ]
display_angles0	number	33.11
display_angles1	string
rsang	number	0.5778785153
rcang	number	0.9929178115
ans	number	744.9648692221
thetaans	number	744.9648692221
phians	number	744.9648692221
area	rational	126984
triples2	list	[ 300, 589, 661 ]
angleDeg	decimal	dec("6.300858665948471587477896863021637435289e+1")
angleRads	decimal	dec("1.099706365353169936361371444772230330574")

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
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​

JME function reference

Description

Some the following were too skinny and so were removed.

random([[3,4,5], [5,12,13], [7,24,25], [8,15,17], [9,40,41],
[11,60,61], [12,35,37], [13,84,85], [15,112,113], [16,63,65],
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[420,851,949], [429,460,629], [429,700,821], [432,665,793], [451,780,901],
[455,528,697], [464,777,905], [468,595,757], [473,864,985], [481,600,769],
[504,703,865], [533,756,925], [540,629,829], [555,572,797], [580,741,941],
[615,728,953], [616,663,905], [696,697,985]])

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `list`

[ 407, 624, 745 ]

→ Used by:

area
d
deltax
h
scale
smallest_angle
tritop
v

Parts

Part a) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add
3. Gap Gap 2. Number entry
  Add
Part b) Gap-fill
1. Gap Gap 0. Number entry
  Add
2. Gap Gap 1. Number entry
  Add

Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

If $ a =$ {triples2[0]}, and $c = $ {triples2[2]}, solve for the angle $\theta$ in degrees to 1 decimal place.

$\theta = $ Gap 0.$^\circ$

Now convert the angle to radians,

$\theta = $ Gap 1.

The area of this triangle is Gap 2.

Advice

Give a worked solution to the whole question.

URL
URL
URL

Text alternative
URL

Text alternative

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exam:

Mixed Trigonometry by Kwame D Dwamena in Kwame D's workspace.

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Error

Trigonometry, finding angles and lengths in right angled triangles

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Bennett Gardiner 5 years, 8 months ago

Bennett Gardiner 5 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

Loading...

Error

Trigonometry, finding angles and lengths in right angled triangles

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Bennett Gardiner 5 years, 8 months ago

Bennett Gardiner 5 years, 11 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`