Question

use the pythagorean theorem to solve each problem.

1. gene and tina build a bike ramp in the backyard for their sister. to the nearest tenth of an inch, how long is the ramp?

20 in.
45 in.

1. a painter leans a ladder against the side of a house. what is d, the distance from the ground to the top of the ladder?

10 ft
3 ft
. what is the value of c in the diagram?
11.

Explanation:

Step1: Apply the Pythagorean Theorem

The Pythagorean Theorem is \(a^{2}+b^{2}=c^{2}\) for a right - triangle. For the bike - ramp problem (assuming it's a right - triangle with legs \(a = 20\) in and \(b = 45\) in), we want to find the hypotenuse \(c\).

$$c=\sqrt{a^{2}+b^{2}}=\sqrt{20^{2}+45^{2}}$$

Step2: Calculate the squares

$$20^{2}=400$$

$$45^{2}=2025$$

Step3: Add the results

$$400 + 2025=2425$$

Step4: Take the square root

$$c=\sqrt{2425}\approx49.2$$

For the ladder problem (assuming a right - triangle with hypotenuse \(c = 10\) ft and one leg \(a = 3\) ft, and we want to find the other leg \(d\)). Using the Pythagorean Theorem \(d=\sqrt{c^{2}-a^{2}}\)

Step1: Apply the Pythagorean Theorem

$$d=\sqrt{10^{2}-3^{2}}$$

Step2: Calculate the squares

$$10^{2}=100$$

$$3^{2}=9$$

Step3: Subtract the results

$$100 - 9 = 91$$

Step4: Take the square root

$$d=\sqrt{91}\approx9.5$$

Answer:

The length of the bike - ramp is approximately \(49.2\) inches. The distance \(d\) from the ground to the top of the ladder is approximately \(9.5\) feet.