a 30 feet ladder resting against a building makes a 60 angle with the ground . find the Height from the ground at which the ladder touches the building to the nearest foot
h = 30*sin60 = 26.0 Ft.
a 18 foot ladder is placed against a building so the angle between the ground and the ladder is 82 degrees. how high does the ladder reach on the building?
To find the height at which the ladder touches the building, we can use trigonometry. In this case, we have a right triangle formed by the ladder, the ground, and the height of the building.
The angle between the ladder and the ground is 60 degrees, and the length of the ladder is 30 feet. We need to find the height (h) from the ground at which the ladder touches the building.
The trigonometric function that relates these values is the sine function: sin(angle) = opposite/hypotenuse.
In our case, the opposite side is the height (h) and the hypotenuse is the ladder length (30 feet).
Therefore, we can write the equation: sin(60) = h/30.
To solve for h, we can rearrange the equation: h = sin(60) * 30.
Using a calculator, we find that sin(60) is approximately 0.866.
Plugging this value into the equation, we get: h = 0.866 * 30.
Calculating this, we get: h = 25.98 feet.
To the nearest foot, the height at which the ladder touches the building is 26 feet.
To find the height at which the ladder touches the building, we can use trigonometry.
In this scenario, the ladder is the hypotenuse of a right triangle, with the height as one side and the ground as the other side.
Given that the ladder is 30 feet long and makes a 60-degree angle with the ground, we can use the sine function to find the height.
The sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In our case, the height is the side opposite the angle, and the ladder is the hypotenuse.
So, the equation is:
sin(60) = height / 30
To solve for height, we need to isolate it, so we multiply both sides of the equation by 30:
30 * sin(60) = height
Using a calculator, the sine of 60 degrees is approximately 0.866, so we can substitute that in:
30 * 0.866 = height
Calculating this, we find that the height is approximately 25.98 feet. To the nearest foot, the ladder touches the building at a height of 26 feet.