Geometry
Grades 9-12
Overview:
Objectives:
Materials:
Procedure:
For this exercise, students will learn how to use cosine,
sine, and tangent of an angle to figure out the length of
missing sides of a right triangle.
Students will be able to:
 Use another method, other than the
Pythagorean Theorem, to find the lengths and
angles of right triangles.
 Use cosine, sine, and tangent of an angle to
figure out the hypotenuse and length of the
missing sides of a right triangle.
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Paper
Pencil
Eraser
Have the students draw 3 right triangles with a
second angle and one side included.
Have students exchange papers and use the sine,
cosine, or tangent necessary to find the rest of
the sides of the triangle.
Exchange papers back to the owner. Have each
student check the others work.
Now have them draw 3 more right triangles but
this time only including two sides of the triangle.
Have the students use cosine, sine, or tangent to
find the angles of the right triangle.
Exchange papers back to the owner. Have each
student check the others work.
Now present a word problem using a right
Evaluation:
Standards:
triangle. Ask a question like, “If a 10 foot ladder
is leaned up against a wall at a 60 degree angle
with the ground, how high up the wall is the top
of the ladder?”
8. Go around checking answers and then go over
the problem.
Now, have the students raise their hands if anyone had
any problems on either of the exercises. If so, go over
and help the student out with his or her problem, or
have him or her propose the problem to the class and
see if any student can solve it. How did they do? Were
they able to use cosine, sine, and tangent to find the
sides and angles of the triangle? Were they able to
understand and answer the word problem?
G.5.4 Define and use the trigonometric functions (sine,
cosine, tangent, cosecant, secant, cotangent) in terms of
angles of right triangles.
G.5.6 Solve word problems involving right triangles.
Standards from: http://dc.doe.in.gov/Standards/AcademicStandards/StandardSearch.aspx
Picture from: http://www.learningelectronics.net/vol_5/chpt_5/1.html