The height of a tree is measured by means of a cross-staff as shown in

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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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.
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Hello,
A prompt question, on the basis of the following "The horizontal bar DE is adjusted up or down until points D, F, and B are in a straight line." we know that angles F and B are equal, however the OE starts by saying that angles C and E are right angles, how can we assume that they are right angles when there is a note saying that the figure is not drawn to scale, I mean we know that C and E are equal because we have the common angle D and the angles F B ( that the problem states are on the same line so they have the same angle) and based on those facts we can deduce that angles C and E are equal, but is it possible to assume that C and E are right angles ? What if DE is not parallel to the ground?
\ <--- (a less steep version of this )

On the GMAT, a triangle inside a triangle is a clear clue that similarity of triangles is being tested in the question.

The two triangles in question here are triangles DEF and DBC. Each of them have a right angle in them and angle D is common. Therefore, triangles DEF and DBC are similar to each other.

Hence, \(\frac{DE }{ DC}\) = \(\frac{EF }{ CB}\).

Now, DC = DE + EC = DE + GA.

Substituting the values given in the question, we have

\(\frac{1.5 }{ 61.5}\) = \(\frac{0.5 }{ CB}\)

Solving, we have CB = 20.5
Answer option A is a trap answer. CB does not represent the height of the tree.

Height of the tree = CB + GE = 20.5 + 5 = 25.5

The correct answer option is D.
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Hello Unstoppable,
Happy to answer your question here.

IMHO, the keyword ‘horizontal’ is a clear give away, isn’t it? Anything that is horizontal is parallel to the ground. So, the line DC is parallel to the ground.

Another keyword that can help us is the word ‘height’. Height of any object is always measured at right angles to the ground.
Therefore, the tree is perpendicular to the ground, which means angle C should be a right angle as well since it is on a line parallel to the ground.

And, as you rightly observed, angles C and E are equal; since C is a right angle, E is a right angle as well.
Hope that answers your question!
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Using Similar triangles : triangle def similar to bcd