8.1.1 Similarity in Right Triangles (continued) Example 4 Measurement Application
The height of an object is calculated from ground measurements in this application example. The distance from the observer to the statue is given, as is her height. Recognize that the lines form a right triangle with an altitude. Let x be the height of the statue above eye-level, or the length of the upper line segment formed by the intersection with the altitude of the large right triangle. Set up a proportion using the ratios of corresponding sides of the similar triangles that includes the unknown length x . Cross multiply and solve for the value of x . Notice that the equation resulting from cross multiplying is the equation for the geometric mean of the lengths of the two line segments formed by the altitude. Solving for x yields an approximate value of 113.6 ft. The statue height includes the height of the observer, so 113.6 + 5.5 = 119.1 feet.
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