A ladder is placed against a wall, with its base 2 m from the wall. The ladder touches the top of a 2 m fence that is 1.5 m from the wall. How high up the wall does the ladder reach?

Question

A ladder is placed against a wall, with its base 2 m from the wall. The ladder touches the top of a 2 m fence that is 1.5 m from the wall. How high up the wall does the ladder reach?

Thanks for answering! Your help is greatly appreciated.

Answer 1

Draw the figure.

Use proportion.

.5/2=2/h

Answer 2

To find out how high 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 length of the hypotenuse (in this case, the ladder) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the base of the triangle formed by the ladder, the wall, and the ground is 2 m, and the side adjacent to the ladder and the fence is 1.5 m.

Let's call the height up the wall "h".

Using the Pythagorean theorem, we have:

2² = 1.5² + h²

Simplifying, we get:

4 = 2.25 + h²

Rearranging the equation, we have:

h² = 4 - 2.25

h² = 1.75

Taking the square root of both sides, we have:

h ≈ √1.75

h ≈ 1.32 m approximately

Therefore, the ladder reaches a height of approximately 1.32 meters up the wall.

Answer 3

To find out how high up the wall the ladder reaches, you can use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled 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 other two sides.

In this scenario, the ladder acts as the hypotenuse of the right-angled triangle, while the distance between the base of the ladder and the wall and the height of the ladder on the wall act as the other two sides.

Let's call the height the ladder reaches on the wall "h". According to the problem statement, the base of the ladder is 2 m from the wall, and the ladder touches the top of a 2 m fence that is 1.5 m from the wall. Using this information, we can set up the equation:

h^2 = (2^2) - (1.5^2)

Simplifying this equation, we get:

h^2 = 4 - 2.25

h^2 = 1.75

Taking the square root of both sides, we find:

h ≈ 1.32 m

Therefore, the ladder reaches approximately 1.32 meters up the wall.

I hope this explanation helps! Let me know if you have any further questions.

Answer 4

The two triangles are similar because they both have a right angle and they share another angle. The triangle is similar through AA~.

H 2 = H= 2 X 1.33= 2.66
2 = 1.5 H=2.66
Therefore, the ladder reaches 2.66m up the wall.