To find the length of the diagonal support x, we will first calculate the length of the vertical support using trigonometry.
Given that the length of the footbridge is 25 feet and the diagonal support makes a 65 degree angle with the vertical support, we can set up a right triangle with the vertical support, the diagonal support, and the footbridge as the hypotenuse.
Let the length of the vertical support be y.
Using the sine function, we have:
sin(65 degrees) = y / 25
y = 25 * sin(65 degrees)
y ≈ 21.71 feet
Now, we can find the length of the diagonal support x using Pythagorean theorem:
x^2 = 25^2 + 21.71^2
x^2 = 625 + 471.69
x^2 = 1096.69
x ≈ √1096.69
x ≈ 33.1 feet
Therefore, the length of the diagonal support x is approximately 33.1 feet.
A 25-foot-long footbridge has two diagonal supports that meet in the center of the bridge.
Each support makes a 65 degree angle with a short vertical support.
What is the length x of a diagonal support, to the nearest tenth of a foot?
1 answer
1 answer