A 20 foot ladder is leaning against a building.If the ratio of the base of the ladder's distance from the building to its top's height from the ground is 3:4, find how high the top of the ladder is from the ground.
Tan A = Y/X = 4/3 = 1.3333.
A = 53.13o.
h = 20*sin53.13 = 16 Ft.
To find the height of the top of the ladder from the ground, let's assign variables to the base and height ratios.
Let the base ratio be 3x (where x is a common factor) and the height ratio be 4x.
According to the problem, the ladder is leaning against the building, forming a right triangle. The base of the ladder represents the horizontal distance from the building, the height represents the vertical distance from the ground, and the ladder itself represents the hypotenuse of the right triangle.
By using the Pythagorean theorem, we can relate the base, height, and hypotenuse:
(base)^2 + (height)^2 = (hypotenuse)^2
(3x)^2 + (4x)^2 = (20)^2
9x^2 + 16x^2 = 400
25x^2 = 400
Divide both sides by 25:
x^2 = 16
Take the square root of both sides:
x = 4
Now, substitute this value back into the height ratio:
4x = 4 * 4 = 16
Therefore, the height of the top of the ladder from the ground is 16 feet.