A bridge 30 m long crosses a chasm. If the bridge is inclined at angle of 20 degrees to the horizontal, what is the difference in height of the two ends of the bridge?
length(sin degree) relative to the horizontal will give you the y or height
To find the difference in height between the two ends of the bridge, we can use trigonometry.
First, let's visualize the problem. We have a bridge that is inclined at an angle of 20 degrees to the horizontal. We can consider the two ends of the bridge as points A and B. The length of the bridge, AB, is given as 30 meters.
To find the difference in height of the two ends, we need to determine the vertical component of AB. This can be done by finding the height of point B above point A.
Using trigonometry, we know that the sine of an angle is equal to the ratio of the opposite side to the hypotenuse. In this case, the height difference between the two ends is the opposite side and the length of the bridge is the hypotenuse.
So, we can use the formula for sine:
sin(20 degrees) = opposite/hypotenuse
sin(20 degrees) = height difference/30 meters
Now, we need to solve for the height difference. Rearranging the equation, we have:
height difference = sin(20 degrees) * 30 meters
Calculating this, we get:
height difference ≈ 10.21 meters
Therefore, the difference in height between the two ends of the bridge is approximately 10.21 meters.