Question

helping answers:
What are the lengths of the side of your patio? "Include units of measure. Leg a= 8ft
Leg b= 6 ft
"Use the pythagorean theorem to find the length of side c (hypotenuse). Show all calculations/work below.
- a^2+b^2 = c^2
-(8 ft)^2 + (6 ft)^2 = c^2 -64 ft^2+36 ft^2 = c^2 - 100 ft^2 = c^2 -c=√100 ft 2 = 10 ft
Side c (hypotenuse): 10
What is the area of your deck? Show all calculations/work below. You will need this answer for
slide 9.
Formulas for area
- Area of a right triangle = (1/2)x base x height -A = (1/2) x 8 ft x 6 ft
- A = (1/2) x 48 ft^2 = 24 ft^2
Reflection- Your answers must be written in full sentences:
✔ PSSA Reference Sheet
Desmos Calculator
Are your side lengths reasonable for creating a garden space to fit at least 3 planters? Why do you think this. A 242 triangular area is large enough to fit at least three planters. For example, three medium planters each with a footprint around 1.5-2 #2 would use about 4.5-6 ft2 total the remaining area allows for spacing between planters and a small path
What do you notice about the hypotenuse of the proposed triangular space compared to the legs? I notice that the hypotenuse (10 ft) is longer than either leg (8 ft and 6 ft).
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question (only do this part using things from helping answers):
Pythagorean Theorem on the Coordinate Plane
1. Take a screenshot of your blueprint on slide 4.
2. Paste the screenshot on top of the blank one below.
3. Use the straight line tool to place an x-axis on your yard (it can go anywhere in the yard!). Make it red and label it the x-axis. 4. Use the straight line tool to place a y-axis on your yard (it can go anywhere in the yard. Make it red and label it the y-axis. 5. Label the vertices of your triangle A, B, C.
34 feet
20 feet
What are the coordinates of your vertices?
A
BO
сс
What are the lengths of the side of your patio? *Include the calulations.
Leg a=
Leg b=
Answer in full sentences.
Tools to choose from: -"count it out"
How would you determine the length of the hypotenuse? Pythago thro
-distance formula?
How did you decide where to place your x and y axis?
Does a side of your patio lie on an axis?

Answer 1

A = (0, 0), B = (8, 0), and C = (0, 6).

The lengths of the sides of the patio are:
- Leg a = 8 ft (AB along the x-axis).
- Leg b = 6 ft (AC along the y-axis).
- Hypotenuse c = 10 ft.

Calculations/work:
- Using the Pythagorean Theorem: a^2 + b^2 = c^2
(8 ft)^2 + (6 ft)^2 = c^2
64 ft^2 + 36 ft^2 = c^2
100 ft^2 = c^2
c = √100 ft^2 = 10 ft.
- Using the distance formula for the hypotenuse BC:
BC = √[(8 − 0)^2 + (0 − 6)^2] = √(64 + 36) = √100 = 10 ft.

I would determine the length of the hypotenuse by applying the Pythagorean Theorem (a^2 + b^2 = c^2) or by using the distance formula on the coordinates of the endpoints of the hypotenuse; both methods give 10 ft.

I decided to place the x- and y-axes so the right-angle vertex is at the origin (0,0) because that makes the two legs lie along the axes and simplifies the coordinates and calculations.

Yes, two sides of the patio lie on an axis: AB lies on the x-axis and AC lies on the y-axis.

(For reference, the area of this right triangle is (1/2)(8 ft)(6 ft) = 24 ft^2.)