An inclined plane lies against the wall. The top of the inclined plane is 8 m above the ground. If the foot of the inclined plane is 4 m away from the wall, how long is the inclined plane? Give non-exact numerical answers correct to 3 significant figures.
Question
An inclined plane lies against the wall. The top of the inclined plane is 8 m above the ground. If the foot of the inclined plane is 4 m away from the wall, how long is the inclined plane? Give non-exact numerical answers correct to 3 significant figures.
Solution
This problem can be solved using the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the inclined plane is the hypotenuse, the height of the plane above the ground is one side of the triangle, and the distance from the foot of the plane to the wall is the other side.
Here are the steps to solve the problem:
- Square the length of each of the two sides: 8^2 = 64 and 4^2 = 16.
- Add these two numbers together: 64 + 16 = 80.
- Take the square root of the result to find the length of the hypotenuse: √80 = 8.944.
So, the length of the inclined plane is approximately 8.944 meters, correct to three significant figures.
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