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22 May 2020, 10:17
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D
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75% (03:09) correct
25%
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The height of a tree is measured by means of a cross-staff as shown in the figure above. The horizontal bar DE is adjusted up or down until points D, F, and B are in a straight line. Measured on level ground, DE is \(1\frac{1}{2}\) feet, EF is \(\frac{1}{2}\) foot, GE is 5 feet and GA is 60 feet. How tall is the tree?
A. \(20 \frac{1}{2}\) ft.
B. \(22\) ft.
C. \(24\) ft.
D. \(25\frac{1}{2}\) ft.
E. \(26\frac{1}{2}\) ft.
PS20369
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22 May 2020, 23:52
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Bunuel
Let us put the data as shown in the sketch.
Now DEF and BDC are similar triangle, so \(\frac{EF}{BC}=\frac{DE}{DC}..........\frac{0.5}{BC}=\frac{1.5}{60+1.5}........BC=\frac{61.5}{3}=20.5\)
Height of tree = \(BC+AC=20.5+5=25.5\)
D
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General Discussion
26 Nov 2020, 17:37
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Bunuel
DE = 1.5 ft
EF = 0.5 ft
GE = 5 ft
GA = 60 ft
Notice that triangle DEF and triangle DBC are similar triangles.
\(\frac{DE}{EF} = \frac{DC}{BC} = \frac{1.5}{0.5} = \frac{61.5}{20.5}\)
\(20.5 + EG = 20.5 + 5 = 25.5 ft\)
Answer is D.
