Trigonometry: Right angled: Find angles to nearest degree (Eukleides version)

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History

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Christian Lawson-Perfect 3 years, 4 months ago

Published this.

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Christian Lawson-Perfect 3 years, 4 months ago

Created this as a copy of Trigonometry: Right angled: Find angles to nearest degree (JSXGraph through JME version).

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

Give any introductory information the student needs.

			Name	Type	Generated Value

triples	list	[ 16, 63, 65 ]
vec1	list	[ 0, 1, 1 ]
v	string
h	integer	63
d	integer	65
scale	rational	8/21
switcharoo	integer	0
tritop	decimal	dec("3.0476")
deltax	decimal	dec("-4.1250")
ansrad	decimal	dec("1.322086337701373749168611993312009390952")
anglelist	list	[ "$\\phi$", 4 ]
angle	string	$\phi$
ans	decimal	dec("7.574996730219641062589594462738344184108e+1")

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random([[3, 4, 5], [5, 12, 13], [7, 24, 25], [8, 15, 17], [9, 40, 41], [11, 60, 61], [12, 35, 37], [16, 63, 65], [20, 21, 29], [20, 99, 101], [24, 143, 145], [28, 45, 53], [33, 56, 65], [36, 77, 85], [39, 80, 89], [44, 117, 125], [48, 55, 73], [51, 140, 149], [52, 165, 173], [57, 176, 185], [60, 91, 109], [60, 221, 229], [65, 72, 97], [68, 285, 293], [69, 260, 269], [75, 308, 317], [76, 357, 365], [84, 187, 205], [84, 437, 445], [85, 132, 157], [87, 416, 425], [88, 105, 137], [92, 525, 533], [93, 476, 485], [95, 168, 193], [96, 247, 265], [100, 621, 629], [104, 153, 185], [105, 208, 233], [105, 608, 617], [111, 680, 689], [115, 252, 277], [119, 120, 169], [120, 209, 241], [120, 391, 409], [132, 475, 493], [133, 156, 205], [135, 352, 377], [136, 273, 305], [140, 171, 221], [145, 408, 433], [152, 345, 377], [155, 468, 493], [156, 667, 685], [160, 231, 281], [161, 240, 289], [165, 532, 557], [168, 425, 457], [168, 775, 793], [175, 288, 337], [180, 299, 349], [184, 513, 545], [185, 672, 697], [189, 340, 389], [195, 748, 773], [200, 609, 641], [203, 396, 445], [204, 253, 325], [205, 828, 853], [207, 224, 305], [215, 912, 937], [216, 713, 745], [217, 456, 505], [220, 459, 509], [225, 272, 353], [228, 325, 397], [231, 520, 569], [232, 825, 857], [240, 551, 601], [248, 945, 977], [252, 275, 373], [259, 660, 709], [260, 651, 701], [261, 380, 461], [273, 736, 785], [276, 493, 565], [279, 440, 521], [280, 351, 449], [280, 759, 809], [287, 816, 865], [297, 304, 425], [300, 589, 661], [301, 900, 949], [308, 435, 533], [315, 572, 653], [319, 360, 481], [333, 644, 725], [336, 377, 505], [336, 527, 625], [341, 420, 541], [348, 805, 877], [364, 627, 725], [368, 465, 593], [369, 800, 881], [372, 925, 997], [385, 552, 673], [387, 884, 965], [396, 403, 565], [400, 561, 689], [407, 624, 745], [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]])
​

JME function reference

Description

Some the following were too skinny and so were removed.

use https://www.mathsisfun.com/numbers/pythagorean-triples.html

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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[23,264,265], [24,143,145], [25,312,313], [27,364,365], [28,45,53],
[28,195,197], [31,480,481], [32,255,257], [33,56,65],
[33,544,545], [35,612,613], [36,77,85], [36,323,325], [37,684,685],
[39,80,89], [40,399,401], [41,840,841], [43,924,925],
[44,117,125], [44,483,485], [48,55,73], [48,575,577], [51,140,149],
[52,165,173], [52,675,677], [56,783,785], [57,176,185], [60,91,109],
[60,221,229], [60,899,901], [65,72,97], [68,285,293], [69,260,269],
[75,308,317], [76,357,365], [84,187,205], [84,437,445], [85,132,157],
[87,416,425], [88,105,137], [92,525,533], [93,476,485], [95,168,193],
[96,247,265], [100,621,629], [104,153,185], [105,208,233], [105,608,617],
[108,725,733], [111,680,689], [115,252,277], [116,837,845], [119,120,169],
[120,209,241], [120,391,409], [123,836,845], [129,920,929],
[132,475,493], [133,156,205], [135,352,377], [136,273,305], [140,171,221],
[145,408,433], [152,345,377], [155,468,493], [156,667,685], [160,231,281],
[161,240,289], [165,532,557], [168,425,457], [168,775,793], [175,288,337],
[180,299,349], [184,513,545], [185,672,697], [189,340,389], [195,748,773],
[200,609,641], [203,396,445], [204,253,325], [205,828,853], [207,224,305],
[215,912,937], [216,713,745], [217,456,505], [220,459,509], [225,272,353],
[228,325,397], [231,520,569], [232,825,857], [240,551,601], [248,945,977],
[252,275,373], [259,660,709], [260,651,701], [261,380,461], [273,736,785],
[276,493,565], [279,440,521], [280,351,449], [280,759,809], [287,816,865],
[297,304,425], [300,589,661], [301,900,949], [308,435,533], [315,572,653],
[319,360,481], [333,644,725], [336,377,505], [336,527,625], [341,420,541],
[348,805,877], [364,627,725], [368,465,593], [369,800,881], [372,925,997],
[385,552,673], [387,884,965], [396,403,565], [400,561,689], [407,624,745],
[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`

[ 16, 63, 65 ]

This variable doesn't seem to be used anywhere.

Parts

Gap-fill
1. Gap Number entry
  Add

Gap-fill

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

Given the triangle described below, the value of {angle} is Unnamed gap $^\circ$ (to the nearest degree).

{max_height(20,triangle())}

Advice

Based on the sides that we have and angle we are interested in we use

$\sin \theta = \dfrac{\text{opposite}}{\text{hypotenuse}}$ $\cos \theta = \dfrac{\text{adjacent}}{\text{hypotenuse}}$ $\tan \theta = \dfrac{\text{opposite}}{\text{adjacent}}$$\sin \phi = \dfrac{\text{opposite}}{\text{hypotenuse}}$ $\cos \phi = \dfrac{\text{adjacent}}{\text{hypotenuse}}$ $\tan \phi = \dfrac{\text{opposite}}{\text{adjacent}}$

and substitute in the values that we have

$\sin \var{anglelist[0]} = \dfrac{\var{v}}{\var{d}}$. $\cos \var{anglelist[0]} = \dfrac{\var{h}}{\var{d}}$. $\tan \var{anglelist[0]}= \dfrac{\var{v}}{\var{h}}$. $\sin \var{anglelist[0]} = \dfrac{\var{h}}{\var{d}}$. $\cos \var{anglelist[0]} = \dfrac{\var{v}}{\var{d}}$. $\tan \var{anglelist[0]}= \dfrac{\var{h}}{\var{v}}$.

To solve this equation for {anglelist[0]} we apply the inverse trig function to both sides to get

$\var{anglelist[0]} = \sin^{-1}\left(\dfrac{\var{v}}{\var{d}}\right)$. $\var{anglelist[0]} = \cos^{-1}\left(\dfrac{\var{h}}{\var{d}}\right)$. $\var{anglelist[0]}= \tan^{-1}\left(\dfrac{\var{v}}{\var{h}}\right)$. $\var{anglelist[0]} = \sin^{-1}\left(\dfrac{\var{h}}{\var{d}}\right)$. $\var{anglelist[0]} = \cos^{-1}\left(\dfrac{\var{v}}{\var{d}}\right)$. $\var{anglelist[0]}= \tan^{-1}\left(\dfrac{\var{h}}{\var{v}}\right)$.

A calculator (in degrees mode) evaluates this as $\var{ans}\ldots^\circ$ which we round to the nearest degree as $\var{precround(ans,0)}^\circ$.

Give a worked solution to the whole question.

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

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Part	Test	Passed?
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Number entry
Number entry		Hasn't run yet

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Trigonometry: Right angled: Find angles to nearest degree (Eukleides version)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Christian Lawson-Perfect 3 years, 4 months ago

Christian Lawson-Perfect 3 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

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Error

Trigonometry: Right angled: Find angles to nearest degree (Eukleides version)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Christian Lawson-Perfect 3 years, 4 months ago

Christian Lawson-Perfect 3 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`