becomes
√
√^3
3
, a simplified version of the tangent of 30 degrees.Additional Examples:a. Pradnya’s kite is 50[U+0080][U+0099]away from her in the sky, forming a 27◦angle with the ground.
Pradnya is 4′6” tall. How high is the kite from the ground?Approximately 30 [U+0080][U+0099]
b. The roof pitch is always described in terms of rise/run. Suppose the roof makes a 65◦with the horizontal truss
and forms the triangle below. How tall is the peak of the roof? 37. 53 [U+0080][U+0099]Arts and Crafts Time!Using paper, have each student create an astrolabe and use it to determine the height of a tall
object, such as a skyscraper or tree.
a. Begin by folding an 8. 5 [U+0080][U+009D]× 11 [U+0080][U+009D]sheet of notebook paper into a square
and remove the excess.
b. Bisect on angle of the square – the segment represents a 45−degree angle.
c. Bisect each 45−degree angle. There should be three creases – two 22.5 degree angles and one 45−degree
angle.
d. Punch a hole in the opposite corner. Tie string through this hole and attach a pencil at the other end.
e. Go outside and line your astrolabe to the top of something, say a tree. Pretend you are hunting and plan to
attack something with your astrolabe.
f. Gravity will show you the degree of your sight.
g. Use trigonometric functions to determine its height.For more information, go to Berkley’s website: http://cse.ssl.berkeley.edu/AtHomeAstronomy/activity_07.html
Sine and Cosine Ratios
Pacing:This lesson should take one to two class periods
Goal:The objective of this lesson is to complete the introduction of trigonometric functions by presenting the sine
and cosine ratios.
Welcome to Camp SOH−CAH−T OA! To make trigonometry fun, invite students to CampSOH−CAH−T OA.
Wear a camp counselor outfit, arrange your students in a circle around a makeshift campfire, and begin with an
old-fashioned tent (one you can use to point out right triangles).
Chapter 1. Geometry TE - Teaching Tips