Final answer:
Using the Pythagorean theorem, the height at which the friend is standing on the wall, with the ladder base 5 meters away and the ladder length of 10 meters, is √75 meters, approximately 8.66 meters.
Step-by-step explanation:
The student is asking about the height up the wall where a friend stands using a ladder. This can be answered using the Pythagorean theorem, which is a principle in mathematics that relates the lengths of the sides of a right triangle.
In this scenario, the wall and the ground form a right angle, with the ladder acting as the hypotenuse of the triangle. Given that the ladder's length (hypotenuse) is 10 meters and its base is 5 meters away from the wall (one of the triangle's sides), we need to find the height (the other side) at which the friend is standing up the wall.
To find the height (h), we apply the Pythagorean theorem (a2 + b2 = c2), where a and b represent the lengths of the two shorter sides of the triangle and c represents the hypotenuse. Plugging in the given values:
52 + h2 = 102,
we can solve for h which gives us:
25 + h2 = 100 => h2 = 75 => h = √75.
Therefore, the height at which the friend is standing is √75 meters, which is approximately 8.66 meters.