Question

Anaya has a rectangular plank of wood that is 32 inches long. She creates a ramp by resting the plank against

wall with a height of 15 inches, as shown.
Using Pythagoras' theorem, work out the horizontal distance between the wall and the bottom of the ramp.
Give your answer in inches to 1 d.p.

Answer 1

To find the horizontal distance between the wall and the bottom of the ramp, you can use the Pythagorean theorem. The horizontal distance is approximately 28.27 inches.

Step-by-step explanation:

To find the horizontal distance between the wall and the bottom of the ramp, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the length of the plank (one side of the triangle) is 32 inches, and the height of the wall (the other side of the triangle) is 15 inches. Let's call the horizontal distance we're trying to find 'x'.

We can set up the equation as follows:

32^2 = x^2 + 15^2

Solving for 'x', we have:

x^2 = 32^2 - 15^2

x^2 = 1024 - 225

x^2 = 799

Taking the square root of both sides, we get:

x = √799

Using a calculator, we find that the square root of 799 is approximately 28.27.

Therefore, the horizontal distance between the wall and the bottom of the ramp is approximately 28.27 inches.

Answer 2

Check the picture below.

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=√(c^2 - o^2) \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{32}\\ a=\stackrel{adjacent}{h}\\ o=\stackrel{opposite}{15} \end{cases} \\\\\\ h=√( 32^2 - 15^2)\implies h=√( 1024 - 225 ) \implies h=√( 799 )\implies h\approx 28.3~in`