Problem 4 Finding Lengths in Similar Triangles

Rock Climbing Before rock climbing, Darius wants to know how high he will climb. He places a mirror on the ground and walks backward until he can see the top of the cliff in the mirror. What is the height of the cliff?

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△ H T V ∼ △ J S V A A ∼ Postulate H T J S = T V S V Corresponding sides of  ∼  triangles are proportional . 5.5 x = 6 34 Substitute . 187 = 6 x Cross Products Property 31.2 ≈ x Solve for  x . table with 5 rows and 3 columns , row1 column 1 , white up pointing triangle h t v , column 2 tilde operator white up pointing triangle j s v , column 3 eh eh tilde operator . cap postulate , row2 column 1 , fraction h t , over j s end fraction , column 2 equals . fraction t v , over s v end fraction , column 3 cap correspondingsidesof . tilde operator . trianglesareproportional . . , row3 column 1 , 5.5 over x , column 2 equals , 6 thirty fourths , column 3 cap substitute . . , row4 column 1 , 187 , column 2 equals 6 x , column 3 cap crosscap productscap property , row5 column 1 , 31.2 , column 2 almost equal to x , column 3 cap solvefor . x . , end table

The cliff is about 31 ft high.

✓ Got It?

4. Reasoning Why is it important that the ground be flat to use the method of indirect measurement illustrated in Problem 4? Explain.