Log inSign up for FREE
Library

Geometry: Unit 5

Last updated 9 months ago
11 questions
Unit 5 - Item 1
Charles is delivering goods from Dawson to Cordele. However, he needs to make a detour to
pick up some necessary supplies in Albany. He knows that it is 23 miles from Dawson to Albany.

1

Part A
If Charles knows that the angle of elevation from Dawson and Albany is 60 degrees, use this information and the map provided to find the distance between Albany and Cordele.

1

Part B
Showing your work, compare the distance traveled by going from Dawson to Albany and then to Cordele with the distance traveled by taking a direct route from Dawson to Cordele. How much time would be saved by the direct route if we assume that he drives an average of 55 mph? If he could pay $45 and have the supplies shipped to Cordele instead, develop an argument for or against making this detour.

Unit 5 - Item 2
A pair of parasailers are sailing at a height of 300 feet in the air while being pulled with a length of rope which has been extended to 500 feet. Use this information to answer the following, round answers to the nearest degree or foot as appropriate.
1

Part A
What is the angle of elevation of the parasailers?

1

Part B
If the angle of elevation changes to 50 degrees, what is the new height of the parasailers assuming the length of rope remains the same.

1

Part C
If the angle of elevation changes to 75 degrees, what is the new height of the parasailers assuming the length of rope remains the same.

1

Part D
Lauren and Brian are discussing how the angle of elevation impacts the height of the parasailers? Lauren says the longer the rope the greater the height. Brian says the greater the
elevation the greater the height of the parasailers. Decide who is correct and provide a counter example.

Unit 5 - Item 3

1

Part A
Identify the sine, cosine, and tangent of angle B. What can we conclude about the sine of angle E? How do you know? What can we conclude about the cosine of angle F? How do you know?

1

Part B
Identify the sine, cosine, and tangent of angle C. What can we conclude about the sine of angle F? What can we conclude about the cosine of angle E?

Unit 5 - Item 4
As a part of their internship, Jose and Laura have been given the job of finding the distance
between a certain scenic overlook and particular cypress tree located along opposite sides of
Georgia’s Providence Canyon. The park service is considering the construction of a suspension bridge to join the two points, and Jose and Laura will be using measurements left behind by a surveyor. However, their project begins with issues as the two are having trouble agreeing on an approach. They know the following information:
  • The measure of angle B between the scenic overlook and a cypress tree on the other side is 56 degrees.
  • The distance between the scenic overlook and an oak tree, directly across from the cypress tree, is 200 feet.
Jose says that they should use the measurements as well as the cosine function to find the
distance across. Laura says they should use the measure of angle A (since it is complementary to angle B) and the sine function to find the distance.

1

Part A
Analyze the difference between the two methods by explaining each process. Please find answers to the nearest foot.

1

Part B
Are the two methods equivalent? How do you know?

1

Part C
Which method would be most efficient? Why?