7.5. Indirect Measurement http://www.ck12.org
Place three markers,O,C,andEon the upper bank of the river.Eis on the edge of the river andOC⊥CE. Go
across the river and place a marker,Nso that it is collinear withCandE. Then, walk along the lower bank of the
river and place markerA, so thatCN⊥NA.OC=50 feet,CE=30 feet,NA=80 feet.
- Is 4 OCE∼4ANE? How do you know?
- IsOC‖NA? How do you know?
- What is the width of the river? FindEN.
Answers:
- Yes.^6 C∼=^6 Nbecause they are both right angles.^6 OEC∼=^6 AENbecause they are vertical angles. This means
4 OCE∼4ANEby the AA Similarity Postulate. - Since the two triangles are similar, we must have^6 EOC∼=^6 EAN. These are alternate interior angles. When
alternate interior angles are congruent then lines are parallel, soOC‖NA. - Set up a proportion and solve by cross-multiplying.
30 f t
EN=
50 f t
80 f t
50 (EN) = 2400
EN= 48The river is 48 feet wide.
Explore More
The technique from the guided practice section was used to measure the distance across the Grand Canyon. Use the
picture below andOC= 72 f t,CE= 65 f t, andNA= 14 , 400 f tfor problems 1 - 3.
- FindEN(the distance across the Grand Canyon).
- FindOE.