Across the River
Part of the Triangles section of Coddy's Geometry journey. Lesson 50 of 63.
Surveyors measure a river they cannot cross with a pair of similar triangles. Stand at A, straight opposite a tree T on the far bank. Walk along the bank to a stake B, then on to C. From C walk straight away from the river until you see B and T in a line: that is D.
The two triangles TAB and DCB have right angles at A and C, and the angles at B are vertical angles, so they are equal. By AA they are similar, with A matching C. Here AB = 15, BC = 5 and CD = 6, so w/6 = 15/5 and the river is 18 m wide.
Challenge
A tree T stands across a river, straight opposite A. The stakes give AB = 20 m and BC = 8 m along the bank, and CD = 12 m straight back from the river, with D, B and T in a line. Find the width AT, then press Check.
Try it yourself
Find the marked part of the figure
Test yourselfThis lesson includes a short quiz. Start the lesson to answer it and track your progress.
All lessons in Triangles
1Sides and Names
Three Sides, Three CornersSorting by SidesNaming by AnglesTicks into EquationsThe Longest SideRecap: Sorting Triangles4Area of a Triangle
Half the RectangleHeight Is Not a SideRight Triangle AreaFinding the HeightAny Side Can Be the BaseRecap: Area10Scale in the World
ShadowsAcross the RiverNested TrianglesA Side with an ExpressionRecap: Scale in the World2The Triangle Inequality
Can Three Sticks Meet?Exactly ReachingThe Range of the Third SideThe FormulaRecap: The Third Side5The Pythagorean Theorem
Squares on the SidesFinding the HypotenusePythagorean TriplesWhen It Is Not WholeRecap: The Hypotenuse3Perimeter
Around the EdgeA Missing SideIsosceles PerimeterSides as ExpressionsRecap: Around the Edge6Finding a Leg
Working BackwardsThe LadderWhich Side Is c?A Leg That Is Not WholeRecap: Finding a Leg