Algebra II
Activity:
Ain’t No River Wide Enough
Posted on May 5, 2008
Topic: Trigonometric Identities
Students simulate the process a surveyor would use to measure the width of a river by measuring length on one side of the river and angles formed by various reference points. They then prove the Law of Sines and apply it to calculate the river’s width, proving that no river is too wide to be measured with trigonometry.
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Activity Key Steps:
In this problem, students investigate a scenario of a team building a bridge. Students work as a team to find some ideas on ways to measure the width.
Students drag the point until they come to the proposed path, where the road intersects the riverbank. They use the intersection command to put a point as a stake between the road and riverbank and label it S2.
Students draw a triangle using their current points. They should see that the triangle is a right triangle and they can use the Law of Sines to find the missing sides.
Students move forward and prove the Law of Sines. The Law of Sines relates the lengths of the sides of a triangle to its angles.
Students walk back by moving the point you to its original position. They calculate the remaining angles of the triangle and then use the Law of Sines to write and solve an equation to find the width of the river.
At the end of this activity, students will be able to prove the Laws of Sines and Cosines to find the unknown sides or angles of triangles.