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McREL Standards Activity

Trigonometry in Action

Purpose:As a result of this activity, students will understand how to apply trigonometry in real-world measurement situations.
Related Standard & Benchmarks:
 Standard 5.Understands and applies basic and advanced properties of the concepts of geometry
   Level IV [Grade 9-12]
   Benchmark 7. Understands the basic concepts of right triangle trigonometry (e.g., basic trigonometric ratios such as sine, cosine, and tangent)
 Standard 4.Understands and applies basic and advanced properties of the concepts of measurement
   Level IV [Grade 9-12]
   Benchmark 3. Selects and uses an appropriate direct or indirect method of measurement in a given situation (e.g., uses properties of similar triangles to measure indirectly the height of an inaccessible object)
Student Product:Calculations showing height of object
Material & Resources:Protractor, tape measure, scientific calculator with trigonometric functions, writing materials
Teacher's Note:This activity is designed to follow an introduction to the basic concepts of right triangle trigonometry. Although tape measures will be easier to use for most situations, if they are not available, students may measure distance using a yard/meter stick. If this is not convenient or practical (due to unven ground), students could measure the distance in ’paces’ and use a yard/meter stick to determine the length of each ’pace’.
Students will work in groups of two or three members. Each group will be assigned an object to measure the height of (e.g., flag pole, building, tree). The group will select a method to determine the angle from their position to the top of the object using the protractor (e.g., using a ruler, piece of paper, or arm to sight along and then determining the angle from the horizontal). They will then use the tape measure to determine the distance from their position to the base of the object. After the measurements have been completed, the students should draw a diagram showing the angle of elevation, distance, and the height at which the angle was measured (i.e., the eye level height of the student measuring the angle). The students will then decide which trigonometric function (i.e., sine, cosine, tangent) to use and solve for the height of the object.