1. 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 tree is 16 feet tall, how tall is the building? (1 point)
A. 32 ft.
B. 8 ft.
C. 24 ft.
D. 16 ft.
Ok so I got some of the answers for the Unit 6 Lesson 8 Test
1. A. 32
2. B. AI=AK
3. A. (5,5)
4. A. I only
5. B. altitude
6. D. <C, <A, <B
7. B. 18 cm, 12 cm, 9 cm
8. B. m<D, m<E, m<F
9. C. It must be greater than 6 and less than 24.
10. B. m<A = m<C
The rest of the questions you'll have to answer because I don't know the answers. SORRY
I hope I was able to help you out :) have a good day
Let's use the concept of similar triangles to solve this problem. Since the rope touches the tree halfway between the stake and the building, we can create two similar triangles: one formed by the rope, tree, and building, and the other formed by the rope, tree, and ground.
Let's denote the height of the building as 'h'. According to the problem, the tree is 16 feet tall, so it acts as the height '16' in both triangles.
Now, let's denote the distance between the stake and the tree as 'd'. Since the tree is growing halfway between the stake and the building, the distance between the tree and the building is also 'd'.
In the first triangle (formed by the rope, tree, and building), the rope acts as the hypotenuse. In this triangle, the height (16 ft) corresponds to the opposite side, and 'd' corresponds to the adjacent side.
In the second triangle (formed by the rope, tree, and ground), the rope acts as the hypotenuse. In this triangle, the height (16 ft) corresponds to the opposite side, and '2d' (as the tree is halfway between the stake and the building) corresponds to the adjacent side.
Since the two triangles are similar, the ratios of corresponding sides are equal. Therefore, we can set up the following proportion:
h/16 = d/2d
Simplifying the proportion:
h/16 = 1/2
Cross-multiplying:
2h = 16
h = 8 ft
Therefore, the height of the building is 8 feet.
The correct answer is B. 8 ft.
To solve this problem, we can use the concept of similar triangles.
Let's assume the height of the building is "x" feet. Since the rope touches the top of the tree and the top of the building, we can form a right triangle with the height of the tree (16 ft), the height of the building (x ft), and the distance between the tree and the building.
Now, let's consider the triangle formed by the top of the tree, the top of the building, and the stake. This triangle is a scaled-up version of the triangle formed by the tree, building, and the distance between them.
Since the tree is halfway between the stake and the building, we can conclude that the distance between the tree and the building is the same as the distance between the stake and the building. Therefore, we can form two similar triangles:
1. Triangle formed by the tree, building, and the distance between them.
2. Triangle formed by the top of the tree, top of the building, and the stake.
Since the height of the tree is 16 feet and the height of the building is "x" feet, the corresponding sides of these triangles are in proportion:
16 ft / x ft = distance between the tree and the building / distance between the stake and the building.
Now, we can solve for x by cross-multiplying:
16 ft * distance between the stake and the building = x ft * distance between the tree and the building.
Since the distance between the stake and the building is the same as the distance between the tree and the building, we can simplify the equation to:
16 ft = x ft.
Therefore, the height of the building is 16 feet.
Answer choice:
D. 16 ft.