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Mathematics |

Posted Wed Mar 9 16:30:18 PST 2005 by Dominick Olivas (dolivas@duarte.k12.ca.us).

Duarte High School, Duarte, United States

Materials Required: Ruler, protractor, scientific calculator, table of trigonometric values

Activity Time: 45 minutes

Concepts Taught: Using the Tangent Ratio

OBJECTIVE:

[To the teacher]After you have done a formal demonstration of how to solve lengths of triangles using the three basic trigonometric functions (Sine, Cosine, and Tangent) this activity will help students apply these skills to real life situations.MATERIALS:

Protractor, scientific calculator or table of trig values, and a rulerTASK:

Without climbing up to the top of the tallest mountain, people can use math to calculate the height. [To the student]Your task today is to calculate the heights of three school landmarks using trigonometry to do so.EXAMPLE: Let's say you want to measure the height of a tall building. Here is a pictorial representation:

/\

** \

** \

** \

** \

** \ o <- this is you!

** \ /I\

** \ /\STEP 1:

Stand away from the building at an angle of your choice (Try 30, 60 or 45), by this you will be able to create a right triangle with the building as the picture indicates. Use the protractor and the ruler to measure the angle from the ground to the top of the building.STEP 2:

Measure the distance between you and the building.STEP 3:

Use the Tangent ratio to set up a proportion to discover the height of the building!The work will look like the following:

::

Angle degrees (d): 30

Distance between you and building: 300 feet

Height of building: x

::Therefore,

tan(d) = opposite side/adjacent side

tan(30) = x/300

0.5774 = x/300

x = 173.21 feetSTEP 4:

Using this as an example, please calculate three landmarks from our school's campus [teacher dicretion! Choose three landmarks that students can measure]OTHER INFORMATION:

This task can be accomplished through collaboration of three group members:PERSON 1:

Measure angle between ground and top of objectPERSON 2:

Measure distance between you and the base of objectPERSON 3:

Use Trig. to calculate the height of the object