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Indirect Measurement with Similar Triangles

Indirect Measurement with Similar Triangles. Similar triangles can sometimes be used to measure unknown lengths or distances indirectly The lengths of corresponding sides of similar triangles are proportional

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Indirect Measurement with Similar Triangles

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  1. Indirect Measurementwith Similar Triangles • Similar triangles can sometimes be used to measure unknown lengths or distances indirectly • The lengths of corresponding sides of similar triangles are proportional • Knowing the length of one pair of corresponding sides allows the lengths of the remaining sides to be found • In the picture at right the person is looking at the reflection of the flagpole in a mirror on the ground • Are the triangles in the picture similar? ∆EXP ~ ∆FXB • What pairs of sides are proportional? EX:FX XP:XB EP:FB • What pair of sides can both be measured? XP and XB • What additional measurement is needed to find the height of the flagpole? The distance EP from the eye to the ground

  2. Indirect Measurementwith Similar Triangles • Another method of indirect measurement with similar triangles uses shadows • To use this method the rays of light must be parallel • Sunlight is one source of parallel rays of light • In the pictures below the shadows of the person and the lamppost are cast on the ground by the sun at the same time • Are the triangles in the picture similar? Yes, by AA • What pairs of sides are proportional? height, shadows • What is the ratio of the sides of the triangles? 1: 3 • What is the value of x, the height of the lamppost? 15.75 ft

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