Question

quiz 1
date ____ pd ____
quiz: pythagorean theorem
show all work as you answer each question. round solutions to the nearest tenth when necessary.

1. a rectangular parking lot has a length of 84 feet and a width of 56 feet. which of the following could be used to find the diagonal distance across the parking lot?

a. $84^2 - 56^2 = c^2$ c. $84^2 + b^2 = 56^2$
b. $(84 + 56)^2 = c^2$ d. $84^2 + 56^2 = c^2$

1. find the missing side length of the right triangle below.

(image of a right triangle with one leg 24 ft, hypotenuse 25 ft)

1. find the missing side length of the right triangle below.

(image of a right triangle with legs 6 in and 12 in)

1. which of the following shows the sides of a right triangle labeled correctly?

a. (image of a right triangle with legs a, b and hypotenuse c) b. (image of a right triangle with legs b, c and hypotenuse a) c. (image of a right triangle with legs a, b and hypotenuse c but right angle at a) d. (image of a right triangle with legs a, c and hypotenuse b)

1. jack has a 35 - foot ladder leaning against the side of his house. if the bottom of the ladder is 21 feet away from his house, how many feet above the ground does the ladder touch the house?

answers

1. ______
2. ______
3. ______
4. ______
5. ______
6. ______
7. ______
8. ______
9. ______
10. ______
11. ______
12. ______

Explanation:

Step1: Select correct Pythagorean formula

The diagonal of a rectangle forms a right triangle with length and width, so use $a^2 + b^2 = c^2$ where $a=84$, $b=56$.
Expression: $84^2 + 56^2 = c^2$

Step2: Calculate missing leg (Q2)

Use $a^2 + b^2 = c^2$, solve for $b$.
Expression: $b = \sqrt{25^2 - 24^2} = \sqrt{625 - 576} = \sqrt{49}$

Step3: Calculate hypotenuse (Q3)

Use $a^2 + b^2 = c^2$, solve for $c$.
Expression: $c = \sqrt{6^2 + 12^2} = \sqrt{36 + 144} = \sqrt{180} \approx 13.4$

Step4: Identify correct right triangle labels

Hypotenuse ($c$) is opposite the right angle.
Check options: Option B has hypotenuse $a$ opposite the right angle.

Step5: Calculate ladder height (Q5)

Ladder is hypotenuse, use $a^2 + b^2 = c^2$, solve for $a$.
Expression: $a = \sqrt{35^2 - 21^2} = \sqrt{1225 - 441} = \sqrt{784}$

Answer:

1. D. $84^2 + 56^2 = c^2$
2. 7 ft
3. 13.4 in
4. B. (Triangle with right angle between sides $b$ and $c$, hypotenuse $a$)
5. 28 feet