Elevation at its Peak

Purpose:  As a result of this activity, students will be able to use trigonometric ratio methods to make indirect measurements of objects. 
Related Standard & Benchmarks:  Mathematics   Standard 5.  Understands and applies basic and advanced properties of the concepts of geometry     Level IV [Grade 912]     Benchmark 8. Uses trigonometric ratio methods to solve mathematical and realworld problems (e.g., determination of the angle of depression between two markers on a contour map with different elevations) 


Student Product:  Sketch and calculation 
Material & Resources:   Scientific calculators
 Topographic map for display (optional)

Teacher's Note:   Some prior instruction in the use of trigonometric ratio methods is a prerequisite to this activity.
 Names and values in the activity can be modified as desired; if displaying a topographic map of the peak in question, be sure to block out its elevation.
 This activity could also be modified so that students take a field trip to a mountain top and take actual measurements themselves; for this they would need a compass and a topographic map. (Again, remember to block out the elevation of the peak in question.)

Activity 
Teachers provide the following information and assignment to students:
"Imagine yourself heading an expedition to determine the elevation of Groaning Mountain, previously unmeasured. Once you have reached the top, you will measure the angle of declination or inclination between Groaning Mountain and the surrounding peaks, which have established elevations. You begin by measuring an angle of declination between Groaning Mountain and nearby Icicle Peak to be 1.66°. You use your topographic map to determine the horizontal distance between the top of Groaning Mountain and the top of Icicle Peak to be 15.5 miles. According to your map, the elevation of Icicle Mountain is 9,854 feet. Using the information you found during your expedition, make a sketch of the two peaks including all of the measurements mentioned above and find the elevation, to the nearest foot, of Groaning Mountain using trigonometric ratio methods; be sure to show your work." 