Trigonometry: Right angled: Find angles to nearest degree

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Ben Brawn

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Ready to use

9 years ago

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Ben Brawn commented 3 years, 4 months ago

Worked solution added

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Ben Brawn 9 years ago

Gave some feedback: Ready to use

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Ben Brawn 9 years ago

Created this as a copy of Trigonometry: Right angled: Find exact angles.

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	[ 276, 493, 565 ]
vec1	list	[ 1, 1, 0 ]
v	integer	276
h	integer	493
d	string
scale	rational	24/493
switcharoo	integer	1
tritop	decimal	dec("6.71805")
deltax	decimal	dec("-8.4275")
ansrad	decimal	dec("1.060431545553259840825805851510370938253")
anglelist	list	[ "$\\phi$", 4 ]
angle	string	$\phi$
ans	decimal	dec("6.07582520227366917048233597524917197045e+1")

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.

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],
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[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`

[ 276, 493, 565 ]

→ Used by:

d
deltax
h
scale
tritop
v

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).

{if(switcharoo=0,triangle(),otherway())}

Advice

Based on the sides that we have and the 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 $\var{precround(ans,8)}\ldots^\circ$ which we round to the nearest degree as $\var{precround(ans,0)}^\circ$.

Give a worked solution to the whole question.

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Trigonometry: Right angled: Find angles to nearest degree

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

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Ben Brawn commented 3 years, 4 months ago

Ben Brawn 9 years ago

Ben Brawn 9 years ago

Error in variable testing condition

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Warning

Generated value: `list`

Parts

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Error

Trigonometry: Right angled: Find angles to nearest degree

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Ben Brawn commented 3 years, 4 months ago

Ben Brawn 9 years ago

Ben Brawn 9 years ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`