A ladder is 2 m long. It leans against a wall so that it is 90 cm from the base of the wall. How far up the wall does the ladder reach? Put your answer in m. Round to 3 sig fig.
First get the same units 2 m and .9 m
wall = x
x^2 + .9^2 = 2^2
x^2 + .81 = 4
solve for x.
To find out how far up the wall the ladder reaches, we can use the Pythagorean theorem. The theorem states that in a right triangle, the square of the lengths of the two legs (a and b) is equal to the square of the length of the hypotenuse (c).
In this case, the ladder is the hypotenuse, the distance from the base of the wall to the ladder is the horizontal leg, and the height up the wall is the vertical leg.
Given that the ladder is 2 m long and the distance from the base of the wall to the ladder is 90 cm, we need to convert the distance to meters.
1 m = 100 cm, so 90 cm = 90/100 = 0.9 m
Using the Pythagorean theorem:
a^2 + b^2 = c^2
Where a = 0.9 m and c = 2 m
(0.9)^2 + b^2 = 2^2
0.81 + b^2 = 4
b^2 = 4 - 0.81
b^2 = 3.19
Taking the square root of both sides:
b = √3.19
b ≈ 1.787
Therefore, the ladder reaches approximately 1.787 m up the wall. Rounded to 3 significant figures, the answer is 1.79 m.
To find out how far up the wall the ladder reaches, we can use the Pythagorean theorem. According to the theorem, in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the ladder forms the hypotenuse, and its length is 2 m. The distance from the base of the wall to the ladder is the other given side, which is 90 cm, or 0.9 m.
Let's call the distance up the wall that the ladder reaches "x" meters. Using the Pythagorean theorem, we can set up the following equation:
(0.9)^2 + x^2 = (2)^2
Simplifying this equation:
0.81 + x^2 = 4
Subtracting 0.81 from both sides:
x^2 = 3.19
Taking the square root of both sides to solve for x:
x ≈ 1.787 m
Therefore, the ladder reaches approximately 1.787 m up the wall.