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Name: ________________________________________________

Honors Pre-Calculus – Portfolio – After Unit 6

PART ONE – AREA ACTIVITY

Your supplies: notebook, protractor, pencil, calculator

Team supplies: 2 tape measures, 26 feet of string

Your goal: create a pentagon with an area of 30 square feet

When you get outside, assemble your team and create your first pentagon. Position teammates to hold the corners of your pentagon in place. Your pentagon must have a perimeter of 25 feet (+ or – 1 foot) and the interior angles must add up to 540° (+ or - 10°). Once your first pentagon is complete and each side and angle has been measured, EACH PERSON IN THE GROUP needs to sketch (roughly) the pentagon in his/her portfolio. The group may then work together to find the area of the pentagon using the method demonstrated in class. Repeat the process at least 2 more times, for a total of 3 pentagons. (If you have time to do more, go for it!)

This activity requires a great deal of cooperation among the members of your team. As you gather data, please make sure that each member in your team has the opportunity to copy down the measurements in his/her own portfolio. You may not move on to your next layout until every member of the team has calculated the area of the previous layout.

At some point before the portfolio is due, write a one paragraph (4-5 sentences) reaction to this activity. Did you learn anything? Did your group function well together? Were the groups too big? Too small? Did your group use a particular strategy to get the area to be close to 30 square feet?

If you follow these directions, you will earn up to 20 points towards your portfolio. Good luck! (

Name: ________________________________________________

Honors Pre-Calculus – Portfolio – After Unit 6

Solve all problems, in order, in your portfolio notebooks. Show all work.

5 points deducted for each day late! Due Date: _________________

Pentagon Activity

See previous handout.

4 (3 pentagons, 1 paragraph) @ 5 points each………… ___ / 20

Trig Word Problems

Solve any six of the following problems, in order, in your portfolio notebooks. Identify them by their original problem number. Draw a diagram for each, and show all work.

6 @ 5 points each ……………………………………………… ___ / 30

1. A ladder of length 16 feet leans against the side of a house. Find the height of the top of the ladder is the angle of elevation of the ladder is 74o.[pic]

2. The length of the shadow of a tree is approximately 125 feet when the angle of elevation of the sun is 33 o. Approximate the height of the tree.

3. An amateur radio operator erects a 75 foot tower for his antenna. Find the angle of elevation to the top of the tower at a point 50 feet from the base.

4. Find the angle of depression from the top of a lighthouse 250 feet above water level to a ship 2 miles offshore.

5. Find the angle of depression from a spacecraft to the horizon if the vehicle is in a circular orbit 100 miles above the surface of the earth. Assume that the radius of the earth is 4000 miles.

6. A train travels 2.5 miles on a straight track with a grade of 1o 10’. What is the vertical rise of the train in that distance?

7. From a point 50 feet in front of a church, the angles of elevation to the base of the steeple and the top of the steeple are 35 o and 47 o 40’, respectively. Find the height of the steeple.

8. From a point 1000 feet in front of a public library, the angle s of elevation to the base of the flagpole and the top of the pole are 28 o and 39o 45’, respectively. If the flagpole is mounted on the front of the library’s roof, find the height of the pole.

9. An airplane flying at 550 miles per hour has a bearing of N 52 o E. After flying 1.5 hours, how far north and how far east has the plane traveled front its point of departure?

10. A ship leaves port at noon and has a bearing of S 27 o W. If the ship is sailing at 20 knots, how many nautical miles south and how many nautical miles wet has the ship traveled by 6 pm?

11. A ship is 45 miles east and 30 miles south of port. If the captain wants to travel directly to port, what bearing should be taken?

12. A pilot is 120 miles north and 85 miles east of an airport. If the pilot wants to fly directly to the airport, what bearing should she take?

13. A surveyor wishes to find the distance from two points across a swamp. She begins by determining that the bearing from the point on the side of the swamp she is to the 2nd point is N 32 o W. Then from the 1st point she walks 50 yards in a direction perpendicular to the segment connecting the 1st and 2nd points. At this point, point 3 the bearing to the 2nd point is N 68 o W. Find the bearing that the surveyor walks from the 1st to 3rd point and find the distance across the swamp, from point 1 to point 2.

14. An observer in a lighthouse 300 feet above sea level spots two ships directly offshore. The angles of depression the ships are 4 o and 6.5 o, respectively. How far apart are the two ships?

15. A passenger in an airplane flying at 30000 feet sees two towns directly to the left of the plane. The angles of depression to the towns are 28 o and 55 o respectively. How far apart are the towns?

16. In traveling across relatively flat land, you notice a mountain directly in front of you. Its angle of elevation to the peak is 3.5 o. After you drive 13 miles closer to the mountain, the angle of elevation is 9 o. Approximate the height of the mountain.

17. A regular pentagon is inscribed in a circle of radius 25 inches. Find the length of the sides of the pentagon. What is its area?

18. A regular hexagon is inscribed in a circle of radius 25 inches. Find the length of the sides of the pentagon. What is its area?

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