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i attached all the requirments that you need in the pictures.

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This activity will give you a little insight into creating a mathematical model and how trigonometry can

be used in the great outdoors.

You will need: a protractor, a piece of string a foot or so in length and some sort of weight to tie at the

end of the string. A printable protractor is also attached.

Skills Set (10 points):

Let F(x)=3x+2. What is the slope that the graph of F(x) makes with the x-axis?

Suppose a line forms an angle with the x-axis whose measure is 0.42 radians. If the x-intercept is

(-3,0), then construct an equation for the line.

• What is similar between the two problems above?

Is more than one answer possible for either problem?

Main Activity ( 20 points):

• Locate a tree near you that is fairly tall. You need to be able to walk to the base and then about

fifty yards away with a clear view of the top of the tree. If you don’t have a tree near you, I’m

sorry to hear that, but you can use a building or a windmill or a castle turret.

• From the base of the tree, or the tall structure you have, pace off about fifty yards. A yard is

about a step if you don’t take huge strides.

• Turn and look at the top of the tree. Estimate the angle between the horizontal and the top of the

tree. This is where the protractor comes in: hold it upside down with one end of the string at

the center. Aim the straight part of the protractor at the top of the tree and let the weight keep

the string vertical. See the attached image ProtractorGuide for a illustration. What is the angle

measure?

Determine the angle measure from the horizontal (as opposed to from the vertical which you just

measured).

• ( 5 points ) You paced off about fifty yards and you know the angle. What is the height of the

tree? (hint: you should be using trigonometry).

• ( 5 points ) Suppose you knew the height of the tree is 24 yards and you are 60 yards away from

the base. How could you ascertain the angle?

• (5 points ) Write a paragraph describing your solution and include a diagram. Remember to be

clear and to use complete sentences. You may mention your function but the point is to write

not state equations.

· ( 5 points) Write a second paragraph that states the species of the tree and name two of its

benefits to the environment. If you are not using a tree, describe the building or turret and two

benefits. Include a picture of your tree in your project report.

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TREE TOP

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GROUND

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Tags:

Skills Test

slop intercept form

coefficient of x

slope of x

intercept slope

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