In this module you have worked with many different trigonometric identities. These identities can be helpful for making precise calculations. For example, you can use identities to find the lengths of the sides of a triangle when the angle measure in standard position is not listed on the unit circle. Most recently you have learned about double-angle and half-angle identities. These are special cases of the sum and difference formulas for sine and cosine. Consider the half-angle identities shown as you work through the scenario below. Sine Half-Angle Identity Cosine Half-Angle Identity 0 1- cose 0 1 + cose sin 2 cos = ± 2 2 Marcus is a craftsman and artist. He uses the knowledge he has gained as an engineering student to create custom pieces. For his current project, he is making a large, intricate, 3-dimensional latticework that will be placed next to the marker which welcomes people to his city. He has the work on the lattice completed. It consists of two long rectangles, such that the bottom rectangle will act as a base for the top rectangle. Together the two rectangles are 12 feet tall. 12 ft In order to help the latticework remain vertical, Marcus will attach two wires to each side of the piece, and affix them to the ground at a point that is exactly 9 feet from the base of the artwork, as shown in the illustration. The measure of the angle of elevation to the top of the base is one-half the measure of the angle of elevation to the top of the latticework. Use this information and what you know about trigonometric ratios and identities to help you explore the questions below. H+ 9 ft

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
Module 11, Half-Angle Identities Assignment
In this module you have worked with many different trigonometric identities. These identities
can be helpful for making precise calculations. For example, you can use identities to find the
lengths of the sides of a triangle when the angle measure in standard position is not listed on the
unit circle.
Most recently you have learned about double-angle and half-angle identities. These are special
cases of the sum and difference formulas for sine and cosine.
Consider the half-angle identities shown as you work through the scenario below.
Sine Half-Angle Identity
Cosine Half-Angle Identity
1- cose
1+ cose
cos = +
sin
= +
2
2
Marcus is a craftsman and artist. He uses the
knowledge he has gained as an engineering student to
create custom pieces. For his current project, he is
making a large, intricate, 3-dimensional latticework
that will be placed next to the marker which welcomes
people to his city. He has the work on the lattice
completed. It consists of two long rectangles, such that
the bottom rectangle will act as a base for the top
rectangle. Together the two rectangles are 12 feet tall.
In order to help the latticework remain vertical, Marcus
will attach two wires to each side of the piece, and affix
them to the ground at a point that is exactly 9 feet from the
12 ft
base of the artwork, as shown in the illustration. The
measure of the angle of elevation to the top of the base is
one-half the measure of the angle of elevation to the top of
the latticework.
Use this information and what you know about
trigonometric ratios and identities to help you explore the
questions below.
9 ft
Transcribed Image Text:Module 11, Half-Angle Identities Assignment In this module you have worked with many different trigonometric identities. These identities can be helpful for making precise calculations. For example, you can use identities to find the lengths of the sides of a triangle when the angle measure in standard position is not listed on the unit circle. Most recently you have learned about double-angle and half-angle identities. These are special cases of the sum and difference formulas for sine and cosine. Consider the half-angle identities shown as you work through the scenario below. Sine Half-Angle Identity Cosine Half-Angle Identity 1- cose 1+ cose cos = + sin = + 2 2 Marcus is a craftsman and artist. He uses the knowledge he has gained as an engineering student to create custom pieces. For his current project, he is making a large, intricate, 3-dimensional latticework that will be placed next to the marker which welcomes people to his city. He has the work on the lattice completed. It consists of two long rectangles, such that the bottom rectangle will act as a base for the top rectangle. Together the two rectangles are 12 feet tall. In order to help the latticework remain vertical, Marcus will attach two wires to each side of the piece, and affix them to the ground at a point that is exactly 9 feet from the 12 ft base of the artwork, as shown in the illustration. The measure of the angle of elevation to the top of the base is one-half the measure of the angle of elevation to the top of the latticework. Use this information and what you know about trigonometric ratios and identities to help you explore the questions below. 9 ft
1. Can you use the given information to calculate the measure of the angle of elevation to the top
of the latticework? If so, find the angle measure to the nearest degree. Show your work. If not,
explain why not and what information is needed.
2. What length of wire will Marcus need to attach the top of the latticework to the ground? Show
your work.
3. Can you use the given information to find the exact height of the base? If so, find the height
and show your work. If not, explain why not and what information is needed.
4. Consider your responses to question 3. Devise a plan to find any information that you need in
order to find the height of the base.
Transcribed Image Text:1. Can you use the given information to calculate the measure of the angle of elevation to the top of the latticework? If so, find the angle measure to the nearest degree. Show your work. If not, explain why not and what information is needed. 2. What length of wire will Marcus need to attach the top of the latticework to the ground? Show your work. 3. Can you use the given information to find the exact height of the base? If so, find the height and show your work. If not, explain why not and what information is needed. 4. Consider your responses to question 3. Devise a plan to find any information that you need in order to find the height of the base.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,