A 25 feet ladder is placed 20 feet away from a lamp post. Find the height of the lamp post.
15 feet
14 feet
17 feet
23 feet
We can use the Pythagorean theorem to find the height of the lamp post.
Let the height of the lamp post be h.
According to the Pythagorean theorem,
(25 feet)^2 = (20 feet)^2 + h^2
625 = 400 + h^2
225 = h^2
Taking the square root of both sides, we get:
h = ±15
Since the height of a lamp post cannot be negative, we can conclude that the height of the lamp post is 15 feet.
Therefore, the correct answer is 15 feet.
To find the height of the lamp post, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the ladder) is equal to the sum of the squares of the lengths of the other two sides (the height of the lamp post and the distance from the lamp post to the ladder).
In this case, the ladder is 25 feet and the distance from the lamp post to the ladder is 20 feet. Let's denote the height of the lamp post as "h".
Using the Pythagorean theorem, we can write the equation:
(20^2) + (h^2) = (25^2)
Simplifying this equation, we get:
400 + h^2 = 625
Subtracting 400 from both sides, we have:
h^2 = 625 - 400
h^2 = 225
Taking the square root of both sides, we get:
h = √225
h = 15
Therefore, the height of the lamp post is 15 feet.