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# Geometry Help!

Use the information in the diagram to determine the height of the tree to the nearest foot.
A. 80 ft

B. 264 ft

C. 60 ft

D. 72 ft

### 3 Answers by Expert Tutors

Bigyan C. | Tutoring For SuccessTutoring For Success
1

so to answer this types of question lets start the concept of similar triangle.

many be you want to recall the concept of similar triangle.

in between two similar triangle the ratio of corresponding are always proportional.

so what do i mean by proportional.

look at the tree and height of the building

if you divide the height of the building by the height of the tree that will yield you one number ( can be any number depensing upon their length). Now if you divide the horizontal length of the building from the base of the building to the point on the group to the left of the building with the length from the base of the tree to the same point on the groud , you will get a number and that must be equal to the number you got before with height division.

And this concept is call proportional.

so

we need a ratio first

so look at the small triangular formed by the tree with that point to its left.

base is 120ft long and hypotenuse is 144 ft long.

did you notice the tree divides the long hypotenuse in two equal part and the base of the tree divides the big base distance from the building to that point to its left in two equal half.

ok so the base of the big triangle formed by the house will be twice as long as 120ft which is 240ft.

now focus on both triangle    they are similar so you can use the similar triangle idea now

so   (height of three/base of the tree) = (height of the building/ base of the building )

(x/120) =( 160/240)       ( no need to write the unit in each step just don't fidget to write the unit at the end :)  )

now you need to do cross multiplication

x and 160 are numerator , and 120 and 240 are denominator

x multiply with 240 and 160 multiply with 120

240x = 19200

divide both side by 240

x = 80 ft

Oliver S. | Skilled, Patient Tutor: Algebra, Geometry, Trig, Precalc, Calc, ACT...Skilled, Patient Tutor: Algebra, Geometr...
5.0 5.0 (75 lesson ratings) (75)
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The key to this problem is to envision there being two triangles, one where the tree is the vertical leg, and one where the building is the vertical leg.  These triangle are similar because they have the same angles as each other, so you can set up a proportion to solve for the height of the tree.

In this setup, the "small" triangle will be the one that includes the tree, and the "big" triangle will be the one that includes the building.  Call the height of the tree x

small/big= small/big

x/160 = 120/240

Cross multiply to get x = 80, so the correct answer is A.

Joseph C. | Joseph, Trilingual instructor, Paso Robles, CAJoseph, Trilingual instructor, Paso Robl...
5.0 5.0 (104 lesson ratings) (104)
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In order to solve this problem, we need to know how far the tree is from the building, however, no such information is given.

Based on the drawing, it appears that the top of the tree is at the midpoint of the building, so its height is 80 feet.