Trig: Diagonal of a parallelogram

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Question statement

{applet()}

The lengths of the sides of parallelogram are $\overline{AB} =\overline{CD} = \var{qty(AB,units)}$ and $\overline{AD} =\overline{BC} = \var{qty(AD,units)}$ , and the known angles are $\theta = \var{theta}^\circ$ and $\phi = \var{phi}^\circ$ .

Determine $\angle{ABC}$ and the length of the diagonal $\overline{AC}$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

			ABC	integer	100
			AC	number	8.451

			Name	Type	Generated Value

theta	integer	45
phi	integer	35
AB	integer	6
AD	integer	5
B	vector	Vector with 2 components
D	vector	Vector with 2 components
C	vector	Vector with 2 components
units	string	ft

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
theta + 90 - phi

JME function reference

Description

angle ABC

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

Can an exam override the value of this variable?

Generated value: `integer`

100

← Depends on:

phi
theta

This variable doesn't seem to be used anywhere.

Parts

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1. Gap $\angle AC$ Engineering Accuracy with units
  Add
2. Gap AC Engineering Accuracy with units
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$\angle ABC = $ $\angle AC$ $\overline{AC} = $ AC

Advice

From geometry:

$\begin{align} \angle ABC &= \theta + (90° - \phi)\\ &= \var{theta}^{\circ} + (90^{\circ} - \var{phi}^\circ) \\&= \var{ABC}^{\circ}\end{align}$

From the law of cosines:

$\begin{align} (\overline{AC})^2&= (\overline{AB})^2 + (\overline{AD})^2 - 2(\overline{AB})(\overline{AD})\cos{\angle ABC}\\&= \var{AB}^2 + \var{AD}^2 - 2 (\var{AB}) (\var{AD}) \cos{\var{ABC}}\\&= \var{qty(siground(AC ^2,4),units+'^2')}\\ \\\overline{AC} &= \sqrt{\var{qty(siground(AC ^2,4),units+'^2')}}\\ &= \var{qty(AC,units)}\end{align}$

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This question is used in the following exams:

Exam 1 Practice Fall 2020 by William Haynes in Online Exams.
ibrahim's copy of 01. Trigonometry Review by ibrahim khatib in MyMaths.
01. Trigonometry Review by Michael Proudman in Engineering Statics.
Fady's copy of 01. Trigonometry Review by Fady Rezk in Fady's workspace.
trig + geometry by abc temp in abc's workspace.
01. Trigonometry Review by Sarah Sojka in Statics at Randolph College.
Jennilyn's copy of 01. Trigonometry Review by Deactivated user in Deactivated user's workspace.
Kopy of 01. Trigonometry Review by Raul Duarte in Raul's workspace.
01. Trigonometry Review by William Haynes in Engineering Statics.

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William Haynes 3 years, 11 months ago

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Generated value: `integer`

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Trig: Diagonal of a parallelogram

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

William Haynes 3 years, 11 months ago

William Haynes 4 years, 1 month ago

William Haynes 4 years, 2 months ago

William Haynes 4 years, 2 months ago

William Haynes 4 years, 5 months ago

William Haynes 4 years, 6 months ago

William Haynes 4 years, 6 months ago

William Haynes 4 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`