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High School — Mathematics
Measurement

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    Measurement

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      Strategies: Advanced Work

      The following activities are suggestions for working with students who are ready for advanced work. We hope that the activities spark ideas and conversations among teachers about useful classroom strategies that can supplement existing curriculum.

      Angle of inclination

      Since students have learned about right triangle trigonometry, they may wonder whether, given the side lengths of a right triangle, they can find the measures of the angles that are non-right. This would be a good opportunity to teach them about the inverse trigonometric functions, whose output is an angle measure.


      Problem

      Helene is 5 feet tall and is standing 15 feet away from a tree that she knows is 45 feet high. What is the approximate angle of her line of sight to the horizon? Provide mathematical support for your solution.

      Method

      We need to find the measure of angle A. Since we can calculate the side opposite angle A and know the side adjacent to angle A, we can use the tangent function to set up the following equation: . Since we need to find the angle, we should use the inverse tangent function: 69°.

      Answer

      The angle of Helene's line of sight to the horizon is about 69°.

      Extension

      Have students create right triangles on paper. Have them measure the side lengths and use the inverse trigonometric functions to predict the angle measures. They can verify their answers using a protractor.

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