A 10 meter ladder is placed against a building at an angle of 75 degree with the ground. how high up the building does the ladder reach?
To find out how high up the building the ladder reaches, we can use trigonometry. In this case, we can use the sine function. The formula is:
sin(angle) = opposite/hypotenuse
In this case, the angle is 75 degrees and the hypotenuse is the length of the ladder, which is 10 meters. We need to find the opposite side, which represents the height up the building.
So, let's apply the formula to find the height:
sin(75 degrees) = opposite/10 meters
Rearranging the equation to solve for the opposite side:
opposite = sin(75 degrees) * 10 meters
Using a scientific calculator, we can evaluate the sine of 75 degrees, which is approximately 0.9659. Plugging this value into the equation:
opposite = 0.9659 * 10 meters
Hence, the height up the building that the ladder reaches is approximately 9.66 meters.