Question

A length of rope is stretched between the top edge of a building and a stake in the ground. The head of the stake is at ground level. The rope also touches a tree that is growing halfway between the stake and the building. If the building is 40 ft tall, how tall is the tree?

a. 20ft
b. 80ft
c. 10ft
d. 18ft

Answer 1

The height of the tree cannot be determined with the given information.

Step-by-step explanation:

The height of the tree can be found by using the concept of similar triangles. Let's assume the distance from the stake to the tree is x ft. Since the tree is growing halfway between the stake and the building, the distance from the tree to the stake is also x ft. From the given information, we know that the height of the building is 40 ft. Using this information, we can set up a proportion:

(40 ft) / (x ft) = (40 ft + x ft) / (x ft + 40 ft)

Cross-multiplying and solving for x:

40(x ft + 40 ft) = (40 ft)(40 ft + x ft)

40x ft + 1600 ft = 1600 ft + 40x ft

40x ft - 40x ft = 1600 ft - 1600 ft

0 = 0

Since 0 = 0, this equation is true for any value of x. Therefore, we cannot determine the exact height of the tree with the given information. The height of the tree could be any value depending on the specific location of the stake and the tree.

Answer 2

GEOM A Unit 6 Test Answers!

1. 20 ft

2. AC = CB

3. (4,4)

4. II only

5. median

6. <B <C <A

7. 6 in, 8 in, 13 in

8. XY < EG

9. 1. BG 2. AC 3. AB

10. 1 < n < 21

11. m<F <m<D <m<E

12. The segment that connects the midpoints of two sides of a triangle is the midsegment. If two objects are the same distance from a point, they are equidistant to the point. If two line segments meet at a 90 degree angle they are perpendicular. If three (or more) lines meet at one point, they are concurrent.

13.

Orthocenter- lines containing altitudes

Circumcenter- perpendicular bisector of sides

Centroid- medians

Incenter- bisectors of angles

14. Circumcenter / Incenter

Contained in the perpendicular bisectors of a triangle- Circumcenter

Equidistant from the vertices of a triangle- Circumcenter

Contained in the angle bisectors of a triangle- Incenter

Equidistant from the sides of a triangle- Incenter

Step-by-step explanation:

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