A ladder 9.00 m long leans against the side of a building. If the ladder is inclined at an angle of 75.0° to the horizontal, what is the horizontal distance from the bottom of the ladder to the building?
The ladder makes a right triangle ABC with the building, where A is the bottom of the ladder, B is a right angle (wall with ground) and C is the top of the ladder.
Now AC = 9 m. and CAB = 75 degrees.
We know that
AB/AC = cos(75) and AC is known.
So AB = AC cos(75) = horizontal distance to the wall.
20 foot ladder is leaning against wall 3 feet out from the house and 12 above the ground how long is the ladder
To find the horizontal distance from the bottom of the ladder to the building, we can use trigonometry.
Let's label the horizontal distance as "x" and the length of the ladder as "9.00 m".
Since the ladder is inclined at an angle of 75.0° to the horizontal, we can use the cosine function to relate the horizontal distance, ladder length, and the angle:
cos(75.0°) = x / 9.00 m
To find x, we rearrange the equation:
x = cos(75.0°) * 9.00 m
Now we can calculate the value of x:
x = cos(75.0°) * 9.00 m
x ≈ 2.333 m
Therefore, the horizontal distance from the bottom of the ladder to the building is approximately 2.333 meters.
To find the horizontal distance from the bottom of the ladder to the building, we can use trigonometry. Let's call this horizontal distance "x".
We know the length of the ladder (9.00 m) and the angle it makes with the horizontal (75.0°). The angle we are interested in is the angle between the ladder and the ground.
In a right triangle, the side opposite to an angle is called the "opposite" side, and the side adjacent to the angle is called the "adjacent" side. In this case, the side opposite to the angle of 75.0° is the height of the building, and the side adjacent to the angle is the horizontal distance we want to find (x).
Now, let's use the trigonometric function called sine (sin) to relate the angle and the sides of the triangle. The sine of an angle is defined as the ratio of the length of the side opposite to the angle to the length of the hypotenuse (the longest side of the right triangle).
In this case, sin(75.0°) = opposite/hypotenuse = x/9.00.
To find x, we can rearrange the equation: x = sin(75.0°) * 9.00.
Using a calculator, we can find the sine of 75.0°, which is approximately 0.9659. Therefore, x ≈ 0.9659 * 9.00 ≈ 8.693 m.
So, the horizontal distance from the bottom of the ladder to the building is approximately 8.693 meters.