Question

name:
pythagorean theorem

• used to find the missing ____ of a ____ triangle.
• sides a and b are called ______.
• side c is called the ______.
• for any right triangle: ______.

directions: find the value of x.
1.
2.
3.
4.
5.
6.
7.

1. scott is using a 12 - foot ramp to help load furniture into the back of a moving truck. if the back of the truck is 3.5 feet from the ground, what is the horizontal distance from where the ramp reaches the ground to the truck?

Explanation:

Step1: Fix Q1 calculation error

Original error: $7^2 + 10^2$ miscalculated. Correct:
$7^2 + 10^2 = x^2$
$49 + 100 = x^2$
$149 = x^2$
$x = \sqrt{149} \approx 12.21$

Step2: Fix Q2 formula error

Use correct Pythagorean form: $x^2 + 19^2 = 21^2$
$x^2 = 21^2 - 19^2$
$x^2 = 441 - 361 = 80$
$x = \sqrt{80} = 4\sqrt{5} \approx 8.94$

Step3: Solve Q3 for leg $x$

Apply $x^2 + 16^2 = 27^2$
$x^2 = 27^2 - 16^2$
$x^2 = 729 - 256 = 473$
$x = \sqrt{473} \approx 21.75$

Step4: Solve Q4 for hypotenuse $x$

Apply $x^2 = 5.3^2 + 12.8^2$
$x^2 = 28.09 + 163.84 = 191.93$
$x = \sqrt{191.93} \approx 13.85$

Step5: Solve Q5 for hypotenuse $x$

Use half the height: $\frac{18}{2} = 9$
$x^2 = 9^2 + 20^2$
$x^2 = 81 + 400 = 481$
$x = \sqrt{481} \approx 21.93$

Step6: Solve Q6 for top side $x$

Find base segment: $\sqrt{19^2 - 17^2} = \sqrt{361-289} = \sqrt{72} = 6\sqrt{2} \approx 8.49$
$x = 31 - 2\times8.49 = 14.02$

Step7: Solve Q7 for side $x$

Find vertical height first: $h^2 = 22^2 - 16^2 = 484-256=228$
Right segment length: $44-16=28$
$x^2 = 228 + 28^2 = 228+784=1012$
$x = \sqrt{1012} = 2\sqrt{253} \approx 31.81$

Step8: Solve Q8 horizontal distance

Let $d$ = horizontal distance: $d^2 + 3.5^2 = 12^2$
$d^2 = 144 - 12.25 = 131.75$
$d = \sqrt{131.75} \approx 11.48$ feet

Answer:

1. $x=\sqrt{149}\approx12.21$
2. $x=4\sqrt{5}\approx8.94$
3. $x=\sqrt{473}\approx21.75$
4. $x=\sqrt{191.93}\approx13.85$
5. $x=\sqrt{481}\approx21.93$
6. $x\approx14.02$
7. $x=2\sqrt{253}\approx31.81$
8. $\approx11.48$ feet