Emaniee would like to build a ramp for her dog over some stairs.
C=(top of stairs) A=(base of stairs) D and A=30
1. Compute the distance between points B and C =21
2. Compute the distance between points A and B=22
3. Compute the distance between points D and B and enter it on your worksheet.
4. Use the Pythagorean Theorem to compute the distance between points D and C.
5. How long does Emaniee's ramp need to be?
To find the distance between points D and B, we can use the Pythagorean theorem:
DB^2 = AB^2 + AD^2
Given that AB = 22 and AD = 30, we can substitute the values into the equation:
DB^2 = 22^2 + 30^2
DB^2 = 484 + 900
DB^2 = 1384
Taking the square root of both sides, we get:
DB = sqrt(1384)
DB ≈ 37.21
Therefore, the distance between points D and B is approximately 37.21 units.
To compute the distance between points D and C, we can use the Pythagorean theorem again:
DC^2 = BC^2 + DB^2
Given that BC = 21 and DB ≈ 37.21, we can substitute the values into the equation:
DC^2 = 21^2 + 37.21^2
DC^2 = 441 + 1384
DC^2 = 1825
Taking the square root of both sides, we get:
DC = sqrt(1825)
DC ≈ 42.77
Therefore, the distance between points D and C is approximately 42.77 units.
Since the length of the ramp represents the hypotenuse of the right triangle with sides DB and DC, the length of Emaniee's ramp needs to be approximately 42.77 units.
To find the length of Emaniee's ramp, we need to find the distance between points D and C. However, we already have the distance between points B and C (21) and the distance between points D and B (which we will compute in step 3). We can then use the Pythagorean Theorem to find the distance between points D and C.
Let's break down the steps:
Step 1: The distance between points B and C is 21.
Step 2: The distance between points A and B is 22.
Step 3: To compute the distance between points D and B, we need to use the information that angle DAB is 30 degrees and we know the length of AB is 22. We can use trigonometry (specifically the sine function) to find the length of DB.
Using the sine function:
sin(DAB) = opposite / hypotenuse
sin(30) = DB / AB
sin(30) = DB / 22
Now we can solve for DB:
DB = sin(30) * 22
Step 4: Now we can use the Pythagorean Theorem to find the distance between points D and C. The theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the hypotenuse is DC, and the other two sides are DB and BC.
Using the theorem:
DC^2 = DB^2 + BC^2
Now substitute the values we have:
DC^2 = (sin(30) * 22)^2 + 21^2
Simplify and solve for DC.
Step 5: The length of Emaniee's ramp is equal to the distance between points D and C, which we found in step 4.
To determine the length of Emaniee's ramp, we need to calculate the distance between points D and C. Let's go step by step.
1. To compute the distance between points B and C, we can use the formula for the distance between two coordinates:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Given that the coordinates of point B are (x2, y2) and the coordinates of point C are (x1, y1), we can replace the values:
distance BC = sqrt((C - D)^2 + (A - A)^2)
= sqrt((30 - D)^2 + (0 - 0)^2)
= sqrt((30 - D)^2 + 0)
= sqrt((30 - D)^2)
= 30 - D (since the square root cancels out the squared term)
So, the distance between points B and C is 30 - D.
2. To compute the distance between points A and B, we can similarly use the distance formula:
distance AB = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Given that the coordinates of point B are (x2, y2) and the coordinates of point A are (x1, y1), we can substitute the given values:
distance AB = sqrt((B - A)^2 + (A - A)^2)
= sqrt((B - A)^2 + 0)
= sqrt((B - A)^2)
= B - A (since the square root cancels out the squared term)
So, the distance between points A and B is B - A, which is 22.
3. Now, we need to compute the distance between points D and B. Unfortunately, the values for D and A are missing, so we cannot calculate this distance without those values. Please provide the values for D and A.
4. To calculate the distance between points D and C using the Pythagorean Theorem, we need the lengths of the other two sides of the right triangle formed by points D, B, and C. Once we have the values for D and B from question 3, we can proceed with this calculation.
5. Once we have the distance between points D and C from question 4, we can add it to the length of the ramp from point C to the ground (A) to get the total length of Emaniee's ramp.