Question

Emaniee would like to build a ramp for her dog over some stairs. The ramp is a right triangle with interior points of 11 and 7 and an outside point of 30 inches next to point D

1. Compute the distance between points B and C and enter it on the worksheet.
2. Compute the distance between points A and B and enter it on the worksheet.
3. Compute the distance between points D and B and enter it on the worksheet.
4. Use the Pythagorean Theorem to compute the distance between points D and
C

Answer 1

[AI-generated answer — Bot GPT 3.5]

To solve this problem, we need to understand the layout of the ramp. Let's assign points as follows:

A - interior point
B - interior point
C - outside point
D - interior point

1. To compute the distance between points B and C, we can use the Pythagorean Theorem. The distance between B and C is the hypotenuse of the right triangle with sides of 30 inches and 7 inches. Using the Pythagorean theorem, we can calculate:

BC = √(30^2 + 7^2) = √(900 + 49) = √949 ≈ 30.82 inches

So the distance between points B and C is approximately 30.82 inches.

2. To compute the distance between points A and B, we can use the Pythagorean Theorem. The distance between A and B is the hypotenuse of the right triangle with sides of 11 inches and 7 inches. Using the Pythagorean theorem, we can calculate:

AB = √(11^2 + 7^2) = √(121 + 49) = √170 ≈ 13.04 inches

So the distance between points A and B is approximately 13.04 inches.

3. To compute the distance between points D and B, we can simply subtract the length of AB from the length of BC, as D lies on the extension of BC. So,

DB = BC - AB = 30.82 - 13.04 ≈ 17.78 inches

So the distance between points D and B is approximately 17.78 inches.

4. To compute the distance between points D and C, we can use the Pythagorean Theorem again. The distance between D and C is the hypotenuse of the right triangle with sides of 17.78 inches and 30 inches. Using the Pythagorean theorem, we can calculate:

DC = √(17.78^2 + 30^2) = √(315.6484 + 900) = √1215.6484 ≈ 34.89 inches

So the distance between points D and C is approximately 34.89 inches.

Let me know if I can help you with anything else.

Answer 2

How long does Emaniee’s ramp need to be?

Answer 3

[AI-generated answer — Bot GPT 3.5]

To determine the length of Emaniee's ramp, we need to find the distance between points A and C, which represents the hypotenuse of the right triangle formed by the ramp.

Using the Pythagorean Theorem, we can calculate the distance between points A and C. The sides of the triangle are 11 inches and 30 inches.

AC = √(11^2 + 30^2) = √(121 + 900) = √1021 ≈ 31.94 inches

So, the length of Emaniee's ramp needs to be approximately 31.94 inches.

Please let me know if there is anything else I can help you with.

Answer 4

[AI-generated answer — Explain Bot]

To answer these questions, we need to first understand the positions and labels of the points in the right triangle.

The given points are:
- Point A: One of the interior points of the right triangle
- Point B: The right angle vertex of the right triangle
- Point C: The other interior point of the right triangle
- Point D: The outside point of the right triangle next to point D

Now let's solve each question step by step:

1. To compute the distance between points B and C, we need to find the length of the side opposite to the right angle, which is the hypotenuse. The distance can be found using the Pythagorean Theorem:

AC^2 = AB^2 + BC^2

Given the coordinates of point A and C are (11,0) and (7,0) respectively, we can calculate the length AC.

AC = sqrt((7 - 11)^2 + (0 - 0)^2)

2. To compute the distance between points A and B, we need to find the length of the side adjacent to the right angle. This can be done using the coordinates of A and B.

3. To compute the distance between points D and B, we need to use the coordinates of D and B.

4. To compute the distance between points D and C using the Pythagorean Theorem, we need to find the length of the hypotenuse. This can be done using the coordinates of D and C.

Once you have the coordinates of the relevant points, you can use the distance formula or the Pythagorean Theorem to find the distances between them.